Johnny Depp asked the Court of Appeal to give permission for him to challenge the damning ruling so the verdict could be overturned and he could have a retrial.
It comes after he lost a libel case against The Sun newspaper in November last year when a column called Mr Depp a “wife beater.”
But on Thursday (March 25), the court refused permission for Mr Depp to appeal against the High Court ruling.
Why wasn’t the verdict overturned?
Mr Justice Nicol dismissed the Hollywood star's libel claim against the publisher of The Sun, finding that an April 2018 column calling Mr Depp a "wife beater" was "substantially true".
The judge ruled Mr Depp, 57, assaulted Ms Heard, 34, on a dozen occasions and put her in "fear for her life" three times following a three-week trial in July last year.
Announcing the ruling at the Royal Courts of Justice in London, Lord Justice Underhill said: "We refuse Mr Depp's application to admit further evidence in support of his proposed appeal and we conclude that the appeal has no real prospect of success and that there is no other compelling reason for it to be heard.
"We accordingly refuse permission to appeal."
What has The Sun said?
In a statement after the ruling, a spokeswoman for The Sun said: "The Sun had every confidence that this leave to appeal application would not be granted and are pleased with today's decision.
"The case had a full, fair and proper hearing, and today's decision vindicates the courageous evidence that Amber Heard gave to the court about domestic abuse, despite repeated attempts to undermine and silence her by the perpetrator.
"The Sun will continue to stand up and campaign for victims of domestic abuse."
Has Amber Heard commented?
A spokeswoman for Amber Heard said in a statement: “We are pleased – but by no means surprised – by the court’s denial of Mr Depp’s application for appeal.
“The evidence presented in the UK case was overwhelming and undeniable.
“To reiterate, the original verdict was that Mr Depp committed domestic violence against Amber on no fewer than 12 occasions and she was left in fear of her life.
“The verdict and lengthy, well-reasoned judgment, including the confidential judgment, have been affirmed.
“Mr Depp’s claim of new and important evidence was nothing more than a press strategy, and has been soundly rejected by the court.”