Depp had sued The Sun over a 2018 article in which he was called a “wife beater” for his alleged abuse of his then wife Amber Heard.
He had vehemently denied the allegations and said it was Heard, 34, who abused him – claims she later denied.
After a three-week trial, Judge Nicol concluded that Depp had beaten Heard 12 times.
Depp’s lawyers had said he would appeal the verdict, which he described in a statement as “evil because confusing.”
The same judge has now dismissed Depp’s appeal, saying he did not believe she had a “reasonable prospect of success.”
In his decision, Justice Nicol wrote: “Findings of fact from a trial court (especially a court, like myself, which has heard oral testimony) are rarely questionable on appeal.
“In any event, I do not consider the proposed grounds of appeal to have a reasonable chance of success (and this is also the case to the extent that the grounds of appeal suggest that I made a mistake of principle or law) and there is no other compelling reason why leave to appeal should be granted. ”
The judge ordered Depp to pay the Sun £ 520,000 for his defense bill by December 7 and an additional £ 108,235 by January 22.
The remainder of the legal invoice will be paid after a detailed cost assessment.
The actor can bring the case directly to the court of appeal.
As part of his findings, the judge found Depp beat Heard 12 of the 14 times he was allegedly violent towards her.
The judge awarded the victory to the publisher, declaring: “I have found that the vast majority of the alleged assaults of Ms. Heard by Mr. Depp have been proven in civil matters.”
Judge Nicol said The Sun and its parent company NGN had proven that what was in the article was “substantially true”.
The judge said: “The plaintiff was unsuccessful in his libel action.
“Although he has proven the necessary elements of his cause of action for libel, the defendants have shown that what they published in the sense that I thought I understood from these words was essentially true.
Mirror Online has reached out to representatives for Johnny Depp and Amber Heard for comment.