Heard, 30, filed for divorce in Los Angeles Superior Court citing irreconcilable differences.
They married 15 months ago and have no children.
They have recently been embroiled in a legal case in Australia after Heard took two dogs into the country illegally. She pleaded guilty in April to a charge of falsifying documents.
Depp, 52, and Heard met while co-starring in the 2011 film The Rum Diary.
In the court papers, Texan-born Heard listed the separation date as Sunday.
Celebrity news website TMZ reported that Depp had asked a judge to reject Heard's claim for spousal support.
The split comes days after the death of Depp's mother. His latest film, Alice Through the Looking Glass, is due to be released on Friday.
The Australian court case started last year when Heard brought two dogs into the country where her husband was filming the latest movie in the Pirates of the Caribbean series.
When the case was settled, the couple released a video apology expressing remorse and advising travellers to respect Australian quarantine laws.
However, Australia's Deputy PM Barnaby Joyce had threatened to have the dogs put down, triggering a war of words with Depp that lasted for months.
The actor recently said on a US TV show that Mr Joyce looks "somehow inbred with a tomato".
Mr Joyce responded by saying he was "pulling strings" in Johnny Depp's head, like film villain Hannibal Lecter.

South Wales Fire and Rescue Service put out the blaze at Alexandra Docks which came after 20,000 tonnes of wood caught alight on 5 December.
The service said four appliances, an aerial platform, two water tankers and a pump had to be sent on Monday after it burst into a fresh blaze.
The fire was eventually was brought under control at about 17:30 GMT.
Six crews remain at the scene damping down.
The fire had been smoking since it started 16 days ago, with Natural Resources Wales saying on 10 December it could continue to smoulder for "weeks".

Wenger, whose club contract runs to the summer, has been linked with the job.
Southgate succeeded Sam Allardyce in September and oversaw England's 2-0 win against Malta as well the disappointing 0-0 draw with Slovenia on Tuesday.
Wenger said Southgate "has accumulated experiences and is a good observer of what's going on in the national team."
Of his own links to the role, the 66-year-old Frenchman added: "I focus on my job, that's what it is about."
Former England international Southgate, 46, has a World Cup qualifier against Scotland at Wembley on 11 November and a friendly against Spain four days later to persuade the Football Association to give him the job on a permanent basis.
Wenger continued: "We're in a job where you get questioned, especially if you have less experience, and the only answer he can give is by showing the decisions he makes are right.
"There's always a demand for big names but the most important thing is the person's competency. He has a good opportunity and I'm happy he has a chance to show he has the quality."
Speaking before his side's game against Swansea on Saturday, Wenger added that 21-year-old defender Hector Bellerin would be offered a new contract by the club.
The Arsenal right-back has been linked with a move, with both Barcelona and Manchester City said to be interested, but Wenger said he was "surprised" by the speculation surrounding the Spain international, who progressed through Barcelona's La Masia academy before joining Arsenal in 2011.
"He has nearly three years to go and we always try get the players to the level where we think they deserve to be. So we try to extend, certainly, his contract," said Wenger.
"For me, his long-term future is here."
Wenger added that midfielder Aaron Ramsey, 25, will miss "one or two" more games, having injured a hamstring during Arsenal's opening-day Premier League defeat by Liverpool on 14 August.
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Film star Johnny Depp and his actress wife Amber Heard are to divorce, US court documents have revealed.
[NEXT_CONCEPT]
A wood chip fire which first ignited at a Newport dockyard more than two weeks ago has flared up again.
[NEXT_CONCEPT]
Interim England manager Gareth Southgate is the right man to take the job on a long-term basis, according to Arsenal boss Arsene Wenger.