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The Hollywood star, 57, took News Group Newspapers to court over counts of libel after The Sun newspaper claimed that he had "beaten" his then-wife Amber Heard, 34.
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.
Depp, who has starred in a number of blockbusters including the Pirates of the Caribbean franchise as well as Charlie and the Chocolate Factory, has repeatedly refuted any allegations of domestic abuse - and has never faced any criminal proceedings over the claims.
Earlier this month, lawyers for Depp requested an appeal at the High Court, stating that their client did not receive a fair trial. They added they had "fresh evidence" about Heard, and claimed she had lied about donating her full $7 million (£5.5 million) divorce settlement to charity.
However, Court of Appeal judges refused Depp's application, saying the original hearing "was full and fair" and that the trial judge "gave thorough reasons for his conclusions which have not been shown even arguably to be vitiated by any error of approach or mistake of law".
Announcing the decision, 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."
"Nor... do we believe that the judge would have reached a different conclusion if it had been established before him that Ms Heard had given a misleading impression about how much of the $7m which she said that she had donated to charity had in fact been paid," the judgement said.
In a statement made after the ruling, a spokeswoman for The Sun told Sky News: "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."
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