Mr Depp, 57, sued the paper after it claimed he assaulted his ex-wife Amber Heard, which he denies. The Sun said the article was accurate.
Judge Mr Justice Nicol said the Sun had proved what was in the article to be “substantially true”.
A spokesperson for the Sun thanked Ms Heard for “her courage”.
The trial was heard over 16 days in July at the Royal Courts of Justice in London.
In a statement, Ms Heard’s lawyer in the US said: “For those of us present for the London High Court trial, this decision and judgement are not a surprise.
“Very soon, we will be presenting even more voluminous evidence in the US.”
Mr Depp is suing Ms Heard in the US in a separate case, over an opinion piece she wrote in the Washington Post. Mr Depp says the article implied he was violent towards her.
‘Depp made Heard fear for life’
In his ruling on Monday, the judge said: “I have found that the great majority of alleged assaults of Ms Heard by Mr Depp have been proved to the civil standard.”
The allegations of violence spanned the period between 2013 and 2016, when the couple split.
In one of the incidents, in Australia in 2015, Mr Depp was allegedly physically and verbally abusive towards Ms Heard while drinking heavily and taking drugs. Mr Depp accused Ms Heard of severing his finger, but the judge said he did not accept Ms Heard was responsible.
“Taking all the evidence together, I accept that she was the victim of sustained and multiple assaults by Mr Depp in Australia,” said Mr Justice Nicol.
“It is a sign of the depth of his rage that he admitted scrawling graffiti in blood from his injured finger and then, when that was insufficient, dipping his badly injured finger in paint and continuing to write messages and other things,” the judge said.
“I accept her evidence of the nature of the assaults he committed against her. They must have been terrifying. I accept that Mr Depp put her in fear of her life.”
Heard ‘not a gold-digger’
The judge said that 12 of the 14 alleged incidents of domestic violence did occur.
The other two included an alleged incident in December 2014, which the judge said he was “not persuaded… constituted a physical assault”, while he said the other in November 2015 could not be proven because it was not put to Mr Depp in cross-examination.
Mr Justice Nicol said that “a recurring theme in Mr Depp’s evidence was that Ms Heard had constructed a hoax and that she had done this as an ‘insurance policy’,” and that Ms Heard was a “gold-digger”.
But he added: “I do not accept this characterisation of Ms Heard.”
Speaking outside court on the last day of the trial in July, Ms Heard said the case had been “incredibly painful” and she just wants to “move on her with her life”.
A spokesperson for the Sun said on Monday: “The Sun has stood up and campaigned for the victims of domestic abuse for over 20 years.
“Domestic abuse victims must never be silenced and we thank the judge for his careful consideration and thank Amber Heard for her courage in giving evidence to the court.”
Charity Women’s Aid said everyone who experiences domestic abuse “deserves to be listened to and believed”.
“This also applies to survivors who do not fit the image of the ‘perfect’ victim – and regardless of the high profile of the alleged abuser. There is no excuse for domestic abuse.”
Mr Depp’s case was brought against News Group Newspapers (NGN) – publisher of the Sun – and executive editor Dan Wootton over an article published on the Sun’s website on 27 April 2018.
The article had the headline: “Gone Potty: How can JK Rowling be ‘genuinely happy’ casting wife beater Johnny Depp in the new Fantastic Beasts film?”
Evidence was heard from both Mr Depp and actress Ms Heard, 34, along with friends and relatives of the ex-couple, and several former and current employees.
The Sun’s publisher said Mr Depp was “controlling and verbally and physically abusive towards Heard, particularly when he was under the influence of alcohol and/or drugs”.
And the Sun’s lawyer argued there is “no doubt that Mr Depp regularly and systematically abused his wife. The characterisation that he is a wife-beater is entirely truthful”.
Mr Depp’s lawyer David Sherborne said his client’s case was about “clearing his name”.
Following the court ruling, Mark Stephens, a lawyer dealing in reputation management, told the PA news agency it was “immensely damaging” for Mr Depp.
“I thought this was an ill-advised action anyway, and it’s just proven to be that.
“Obviously there are serious findings of act against Johnny Depp: that the judge believes that he was a wife beater, that he was a habitual user of drugs and alcohol – and obviously one hopes that he gets the help that he obviously needs,” he said.
Source:BBC