In newly filed court documents as part of his $50m (£39m) defamation case against her, Depp accused Heard of having "painted-on bruises".
"I have denied Ms Heard's allegations vehemently since she first made them in May 2016," he said.
A lawyer for Heard denied the allegations against his client.
Depp launched the defamation case against Heard after the actress described herself as the victim of domestic abuse in a piece in the Washington Post in December.
Heard asked a judge in Virginia to dismiss the lawsuit, prompting the new declaration from Depp.
"I have denied Ms Heard's allegations vehemently since she first made them in May 2016 when she walked into court to obtain a temporary restraining order with painted-on bruises that witnesses and surveillance footage show she did not possess each day of the preceding week.
"I will continue to deny them for the rest of my life."
Depp added: "I never abused Ms Heard or any other woman.
"She was the perpetrator, and I was the victim. While mixing prescription amphetamines and non-prescription drugs with alcohol, Ms Heard committed innumerable acts of domestic violence against me, often in the presence of a third-party witness, which in some instances caused me serious bodily harm."
In a statement to People magazine, Heard's lawyer Eric George said: "The evidence in this case is clear: Johnny Depp repeatedly beat Amber Heard.
"In light of the important work done by the #TimesUp movement highlighting the tactics abusers use to continue to traumatise survivors, neither the creative community nor the public will be gaslit by Mr Depp's baseless blame-the-victim conspiracy theories."
A spokesperson for Depp, in a statement given to the BBC, accused Heard of an "infamous hoax" which he said had been "obliterated", adding: "Amber Heard's lawyer says 'the evidence in this case is clear,' and then presents none."
Depp and Heard started dating after meeting on the set of 2011 comedy The Rum Diary. They married in Los Angeles in February 2015.
The BBC has contacted Depp and Heard's representatives for comment.
Heard obtained a restraining order against Depp after accusing him of abuse in May 2016, which he denied.
The couple settled their divorce out of court in 2016 and both actors signed non-disclosure agreements barring them from discussing their relationship publicly.
In a joint statement issued at the time, they said their relationship was "intensely passionate and at times volatile, but always bound by love".
They added: "Neither party has made false accusations for financial gain. There was never any intent of physical or emotional harm."