Depp sued News Group Newspapers (NGN),The Sun's publisher, over accusations he was violent towards Ms Heard, but the newspaper insisted its article had been accurate.
The libel claim was rejected by Mr Justice Nicol, who said The Sun's claim was "substantially true", ruling in the newspaper's favour.
The judge found the 57-year-old, had assaulted Heard on a dozen occasions and put her in "fear for her life" three times, but the verdict was only made public last November.
