At a hearing in London's High Court, Mr Justice Tugendhat said she wrongly identified Lord McAlpine as a paedophile through innuendo.
Bercow controversially wrote "Why is Lord McAlpine trending? *Innocent face*" in a tweet just a few days after the BBC's Newsnight screened a report compiled by the Bureau of Investigative Journalism. The programme wrongly linked "a leading Conservative politician from the Thatcher years" to a child sex abuse scandal at a children's home in Wales during the 1970s and 1980s.
Although Newsnight did not name the accused politician, the report kickstarted a flurry of denigratory speculation on and offline.
And after ITV's This Morning presenter Phillip Schofield handed the Prime Minister a list of supposedly alleged paedophiles with Lord McAlpine's name clearly visible, live on telly, the Tory peer's identity began trending on Twitter - leading to Bercow's ill-judged tweet.
There is no suggestion of any wrongdoing by Lord McAlpine, who subsequently won a six-figure libel payout from the BBC and ITV.
The peer then took Bercow to the High Court, claiming her tweet was defamatory. She contested the allegation, but will now accept an offer to settle out of court following today's judgment against her.
In his full ruling, Mr Justice Tugendhat stated:
The applicable law is well established and not in dispute. As a matter of law, words are defamatory of a claimant if (1) they refer to that claimant and (2) they substantially affect in an adverse manner the attitude of other people towards the claimant, or have a tendency so to do.
It follows that, for these reasons, I find that the Tweet meant, in its natural and ordinary defamatory meaning, that the Claimant was a paedophile who was guilty of sexually abusing boys living in care.
If I were wrong about that, I would find that the Tweet bore an innuendo meaning to the same effect. But if it is an innuendo meaning it is one that was understood by that small number of readers who, before reading the Tweet on 4 November, either remembered, or had learnt, that the Claimant had been a prominent Conservative politician in the Thatcher years.Lord McAlpine's solicitor Andrew Reid said the ruling "is one of great public interest and provides a warning to, and guidance for, people who use social media".
According to Press Gazette, Reid said: "The failure of Mrs Bercow to admit that her tweet was defamatory caused considerable unnecessary pain and suffering to Lord McAlpine and his family over the past six months. With knowledge of the judgment I am pleased to be able to say that Mrs Bercow has finally seen sense and has accept an offer of settlement which Lord McAlpine made back in January."
After the defamatory rumours began swirling on social networks, Lord McAlpine threatened to sue hundreds of Twitter users who had libelled him, before focussing his attention on those with more than 500 followers. He then zeroed in on Bercow.
Her defence claimed the phrase "innocent face" was intended to help netizens imagine a deadpan expression on her fizog. She also claimed it infered she was "asking it in a neutral and straightforward manner".
In a statement issued after the ruling, Sally Bercow said:
In November 2012 I tweeted the question 'why is Lord McAlpine trending? *innocent face*'. I did not tweet this with malice, and I did not intend to libel Lord McAlpine.I was being conversational and mischievous, as was so often my style on Twitter. Today the High Court found that my tweet constituted a serious libel, both in its natural meaning and as an innuendo. To say I am surprised and disappointed by this is an understatement. However, I will accept the ruling as the end of the matter.
I remain sorry for the distress I have caused Lord McAlpine and I repeat my apologies. I have accepted an earlier offer his lawyers made to settle this matter."Today's ruling should be seen as a warning to all social media users," she added. "Things can be held to be seriously defamatory, even when you do not intend them to be defamatory and do not make any express accusation. On this I have learned my lesson the hard way."