Depp, 57, has said he will appeal the decision, with his legal team calling it "as perverse as it is bewildering."
He took legal action against News Group Newspapers, which publishes The Sun, and its executive editor, Dan Wootton, who wrote an article in 2018 saying Depp had been violent toward his ex-wife, actress Amber Heard, on at least 14 occasions.
Both Depp and Heard, 34, gave evidence during a three-week hearing at London's High Court in July, a high-stakes case that drew worldwide attention as it laid bare the details of their private lives.
Depp's legal team said he was "entitled to very substantial damages" because of the harm to his reputation caused by the allegations, which he denied and labeled as a "hoax."
But on Monday, Justice Andrew Nicol said that News Group Newspapers and Wootton "have shown that what they published ... was substantially true."
Nicol said in his written judgement, "I have found that the great majority of alleged assaults of Ms. Heard by Mr. Depp have been proved to the civil standard."
Jenny Afia, a partner at the law firm Schillings who is representing Depp, said, "The judgment is so flawed that it would be ridiculous for Mr. Depp not to appeal this decision."
Afia said the judge had relied too heavily on Heard's testimony, while disregarding a "mountain of counter-evidence" from police, medical practitioners and documentary sources, which "completely undermined the allegations."
Following the result, Heard's lawyer Elaine Charlson Bredehoft said in an emailed statement, "For those of us present for the London High Court trial, this decision and judgment are not a surprise."
Bredehoft added, "Very soon, we will be presenting even more voluminous evidence in the U.S. We are committed to obtaining justice for Amber Heard in the U.S. court and defending Ms. Heard's right to free speech."
Stricter libel laws in the United Kingdom mean that the burden is on the defendant to prove that their allegations are true.
Depp had told the court he was never violent toward Heard, who he met in 2011 and married in 2015. Heard filed for divorce after just 15 months, and days later obtained a restraining order against him, the court was told.
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Depp instead insisted that she had regularly attacked him, telling the court that he lost the tip of a finger after she threw a vodka bottle at him during an argument.
His lawyer, David Sherborne, argued Heard was a "wholly unreliable witness" and a compulsive liar. And Depp's former long-term partner Vanessa Paradis and his ex-girlfriend actress Winona Ryder gave witness statements saying he was never violent toward them.
The judge said he found that the case presented by the Sun's lawyers was in fact correct. They had told the court they had shown Depp had beaten Heard during violent rages brought on by alcohol or drugs. They said he assaulted Heard on at least 14 occasions between 2013-16.
Heard said in written testimony that Depp "explicitly threatened to kill [her] many times," and that he subjected her to "punching, slapping, kicking, head-butting and choking" during their time together.
Reuters contributed to this report.