Kate and Johnny met at the Cafe Tabac in New York City in January of 1994. Kate was asked in an interview for Spin magazine if it was love at first sight. She said, "No, not the first moment I saw him. I knew from the first moment we talked that we were going to be together. I've never had that before."
Johnny and Kate premiered their relationship at a party held at the Smashbox in Los Angeles on February 15, 1994, where a short film called "Banter" directed by Johnny was also premiered. The party was to benefit Drug Abuse Resistance Education (D.A.R.E.). Johnny thanked Kate for her help on the film in the ending credits. This was the first time pictures were taken of the duo. Up until this point, there was a great deal of speculation by the tabloid press regarding their relationship particularly regarding their stay together at the Royalton Hotel during a snow storm in New York during early February.
The affectionate couple were photographed by a fellow vacationer at the island of St. Bart's in March of 1994. During the vacation, they took a trip on a luxury yacht. According to bystanders, the couple was very passionate, sharing lingering kisses and had eyes only for each other.
Upon their return to New York on April 5, 1994, a very tan Johnny and Kate attended the premiere of John Water's movie, "Serial Mom". 
Also in New York in April, they attended an invitation only performance by Johnny Cash at the Fez club. Mr. Cash appeared at the Viper room in March which led to his association with Kate and her appearance in his video, "Delilah's Dead".
In May, Johnny attended a fashion show by Isaac Mizrahi to benefit AIDS Project L.A. at Mann's Chinese Theatre in Hollywood to see Kate on the catwalk for the first time. Johnny, Kate and Linda Evangelista left the party early and were later spotted at the Viper Room where the lower-level was closed for a private party. Also, in 1994, Kate and Johnny attended the launch party for Naomi Campbell's book, "Swan" at the Tramp club in London.
September 13, 1994, the event that will always be associated with their relationship occurred. Johnny trashed his hotel room at the Mark Hotel in New York with Kate present in the room. This incident set off a frenzy of speculation, rumor and innuendo in the tabloid press as well as the legitimate (?) press. 
Surely, Kate and Johnny were through. NAW! On September 24, they appeared together and quite affection at the premiere of Johnny's movie, "Ed Wood" at the New York film festival. The next day they graciously attended a Pediatric AIDS Foundation carnival where they manned a hockey game booth and assisted children in tossing balls for the game. Later that evening Johnny threw an enormous birthday party for Actor Mickey Rourke at the Metronome on Broadway in New York. Kate arrived at the party later in the evening and had to be rescued and whisked upstairs to Johnny by her brother Nick.
Over the Christmas holiday in 1994, Johnny and Kate vacationed in Aspen. They reportedly rented a house outside of Aspen and were seen walking arm in arm through the streets of Aspen window shopping. In the UK Elle, Kate said this about skiing in Aspen, "I was alright, actually. I got on these skis and I was, like, a natural. I was good, I was. It was really funny. Yeah, I had a laugh."
For Kate's 21st birthday 1995, Johnny threw a surprise birthday party at the Viper Room. Kate had this to say about the party in the 5/95 issue of the UK Elle magazine, "They opened the curtains and there was my mum, my dad, and everyone had flown in from London and New York and John (Galliano) had come from Paris, it was amazing. I was like, shaking - you know when you start to dance and your legs don't work? I had to go into the office for 10 minutes till I'd calmed down." Thelma Houston and Gloria Gaynor sang for her. "Gloria Gaynor said, "Happy birthday Miss Moss" - I was like, 'Oh my God! I hated it," says Moss, grinning. "Johnny said, We're going to dinner" - he's like, Put a dress on" and I'm like, I haven't got a dress. So I had on this satin dress down to the floor, and he got the scissors and he's, like, cutting it up to the knee, literally, while we're walking out the door. I'm wearing, like, red satin up to the knee, all jagged."
Kate and Johnny attended the Golden Globe Awards Show in January, 1995. Johnny was nominated for his portrayal of Ed Wood. At the show, Kate and Johnny sat at a table with director Tim Burton and Actor Martin Landau.
Johnny and Kate attended the premiere in April 1995 of Johnny's movie, "Don Juan DeMarco."
Kate premiered photos from her coffee table book, "The Kate Moss Book" at a reception held at the James Danzinger Gallery in New York City on September 11, 1995. At the party Johnny was asked if he took pictures. "Yeah, I take pictures," he said. "I take polaroids of my dog." He was asked if he ever focus on Kate? "No, it's just the dog," laughed Kate. "We're obsessed with the dog." (Vanity Fair 11/95). Also at the party Johnny held up a poster opposing French nuclear testing. "Don't buy French! Don't buy French!" Kate yelled above the din as she waved a glass of bubbly around. "Oh dear," she said, catching herself. "I'm drinking Champagne, and all Champagne is French, isn't it?" She pondered this irony for a moment. "Well, it's only a gallery opening," she said, "so maybe it isn't." (New York Times 9/17/95)
Kate and Johnny were together during New York's Fashion Week which began on November 5, 1995. According to the NY Daily News, Johnny and Kate were to be at the premiere of a short film directed by Johnny on 11/11/95 at the 212 Group party at Industria. The film was about French nuclear testing which Johnny and Kate are vehemently against. They also appear in nuclear-free South Pacific posters plastered all over London.
On 11/17/95, Johnny participated in a chat for America Online. This question was posed to him, "Johnny, are you still talking to Kate Moss?". Johnny's answer, "As of about 3 minutes ago, yes". Also, on 11/20/95, Johnny escorted his mother to the premiere of his new movie and was quick to tell the press that Kate was in Japan working. The above contradicted tabloid rumors that they were seperated. However, there continued to be periodic reports in the press that Johnny and Kate had split.
As to the rampant rumors in August and September, 1995, regarding an impending wedding for Kate and Johnny, Kate said in a 10/95 interview with Entertainment Tonight when the marriage question was posed, "He's just my boyfriend. That's all. We're not getting married". In an interview with Playboy (1/96), Johnny said about the marriage rumors, "It's fiction. I can guarantee you that if I woke up one day with a wild hair up my ass to get hitched, there wouldn't be invitations. We'd run out and do it."
Johnny and Kate were in Aspen together again over the Christmas holiday (1995). They were seen together at a nightclub called The Caribou Club. Kate was seen skiing with her brother, Nick. And Johnny was supposedly working out with a trainer to get ready for his next movie. They also were together in Florida on January 11, 1996, at a party given by Island Records mogul, Chris Blackwell, at his hotel in South Beach. On Kate's 22nd birthday, January 17, 1996, Johnny hosted a party at a restaurant in London which was attended by about 40 people. Johnny paid for the entire party.
Again in early February, 1996, their were tabloid reports that the duo had parted. This time the reports said that Kate was tired of Johnny not paying enough attention to her and she wanted to date other men. Johnny reportedly went to his mother's farm to plan how to win Kate back. But the pair was
together during fashion week in New York City in March, 1996. Johnny was in
New York filming "Donnie Brasco" during the fashion shows. He attended the
"Vegas" party hosted by Kate and Naomi Campbell on March 29th. The party
raised money for Cancer research. In early June, Johnny and Kate were seen
dancing together at the wrap party for "Donnie Brasco".
According to an interview in Select magazine with Noel Gallagher of Oasis, Johnny and Kate were in Mustique with Noel and his girlfriend, Meg. Meg and Kate are long time-friends and Kate often stays with them when she is in Great Britain. 
During their vacation together, Noel was writing songs for his new album and Johnny was writing the script for his directorial debut, "The Brave". The ladies were evidently just hanging out and disgusted with the lack of attention they were receiving from their gentlemen friends. Johnny and Kate were together on November 11, 1996, in New York at a party for author Hunter S. Thompson.
It was been reported from several sources that Johnny moved in with Kate in December, 1996 at her apartment in New York. Johnny and Kate attended the premiere of "Donnie Brasco" together in Los Angeles on February 24th, 1997. Kate also attended with Johnny the premiere of his film "The Brave" in Cannes on May 10th, 1997, during the 50th anniversary of the Festival.
Tabloid news the week of June 16, 1997, suggests that Kate and Johnny had again split. There was no confirmation about this from Kate or Johnny.
The rumor began in the London Sun newspaper on 6/16 when they reported - "Supermodel Kate Moss has finally split from Hollywood hell-raiser Johnny Depp. The couple are going their separate ways after a stormy four-year relationship. A source said they planned to remain friends and Kate will go to Depp's film premiers. Kate, 23 from Croydon, South London, had once talked about marrying the Edward Scissorhands star. Earlier this year, Depp 33, moved into Kate's New York flat. But instead of cementing the relationship, the couple found they got on each others nerves." The June 23 New York magazine added this to the Sun rumor - ..."According to fashion-world insiders, Kate has told friends that she called it quits with the hot-tempered heartthrob last week because they were having too many fights. Says the source, "They've had small separations before, but this was a major breakup...Depp's spokesperson didn't return calls; Moss's publicist declined to comment on his client's personal life..." On 6/25 the New York Post had this to add to the rumors - "...Sources say things were already rocky for the couple back in May at the Cannes Film Festival. They rented separate villas. Kate shared one with her pals from Oasis...and they never visited each other's pad. Friends say Kate wants to keep the relationship alive, but Johnny won't change to suit her...When Depp was in town recently, the pair didn't even see each other once. Depp's publicist Nancy Seltzer still maintains, "to our knowledge the breakup is untrue." On June 26th Mitchell Fink of People magazine had this to say - "...According to friends, Moss wants to continue to date Depp occasionally, but Depp isn't into open relationships. For the record, a Depp spokeswoman says, "To our knowledge [news of] the breakup is untrue." Janet Charlton of Star magazine said on the E! Gossip show that Kate and Johnny had taken a vacation from one another while Johnny continues working on improving "The Brave" and will resume their relationship when he is through. And that Winona Ryder has been calling Johnny since she still cares for him and that Kate should watch out. (That definitely sounds like gossip.) And last, The New York Post reported on June 27th that - "...Moss has taken up with 32-year-old Tarka Cordell...and that he and Kate were making a chump out of Johnny long before he gave the waif her walking papers. Sources say that for the past year Cordell has stayed at Moss' apartment in New York whenever he's in town...'To my knowledge they've been friends for a while,' says Paul Rowland, owner of Moss' agency, 'but I don't think there's any romance involved.'" Also the Star magazine had an article about a wild night Johnny supposedly had with Demi Moore but that one isn't worth my typing efforts. So there you have the gossip.
Johnny and Kate were together for a Rolling Stone Concert in New York on January 16, 1998. The Daily News had this to say about the event -
"Johnny Depp and Kate Moss appear to be back together. The fun couple joined Uma Thurman and Ethan Hawke at the Rolling Stones Concert on Friday. Exiting Madison Square Garden, Depp was in high spirits. When paparrazzo John Barrett dropped his house keys, Depp picked them up, then asked Barrett to "prove" they belonged to him. Barrett did, prompting Depp to toss them back on the sidewalk"
This mention appeared in the New York Magazine dated February 2 1998 -
"Stones Fan Gathers No Moss At least one supermodel makes it to her appointments on time. Kate Moss had promised record mogul and friend Chris Blackwell that she would attend the opening of the Aveda spa at his Strawberry Hill resort in Jamaica. What the prototypical waif didn't bargain for was how long her 24th-birthday celebration with ex-beau Johnny Depp would last. The pair began the evening at the Madison Square Garden Rolling Stones show and then headed back to guitarist Ron Wood's Palace Hotel suite for an all-night bender with Helena Christensen and Keith Richards's son Marlon. The crew was spotted roaming the halls till sunrise. But that morning, like a trouper, Moss raced to the airport, hopped a commercial jet to Kingston, and helicoptered into Strawberry Hill. She spent just four hours there before heading back to New York. Blackwell said affectionately, "She looked like she had been through hell, but I was impressed that she kept her word and decided to show."
In an interview with ICON magazine June 1998, Johnny mentioned that he is single. When asked if it was strange seeing Kate's picture on billboards, he said, "No, it's nice, you know? It's nice to be able to sort of drive by and wave, say hi. It's sweet. I like seeing her face."
Kate and Johnny were together for the premiere of Johnny's movie, "Fear and Loathing in Las Vegas", in Cannes on May 15, 1998.
In another interview for the New York Daily News 5/17/98, Johnny said the following about his relationship with Kate: "Kate is somebody I care about deeply. We were together for four years, and she's a great, lovely, sweet, pure girl, really a great kid, and I care about her. I love her on a very deep, profound level. Distance is very difficult when you're trying to maintain a relationship, when you're thousands of miles apart for a lot of time. We still see each other, hang out and talk on the phone. We're close, but I'm not with anybody at all."