Sally Bercow said the High Court's ruling that her tweet about Lord McAlpine was libellous "should be seen as a warning to all social media users".
Mrs Bercow said in a statement that she did not write the tweet "with malice" and "did not intend to libel" the Conservative peer.
I was being conversational and mischievous, as was so often my style on Twitter.
I very much regret my tweet, and I promptly apologised publicly and privately to Lord McAlpine for the distress I caused him. I also made two offers of compensation.
Lord McAlpine issued proceedings and the last few months have been a nightmare. I am sure he has found it as stressful as I have. Litigation is not a pleasant experience for anyone.
Sally Bercow said she has "accepted an earlier offer" made by Lord McAlpine's lawyers "to settle this matter" after the High Court ruled a tweet she wrote about the Conservative peer was libellous.
Sally Bercow said she was "surprised and disappointed" after the High Court ruled a tweet she wrote about Lord McAlpine was libellous.
Mrs Bercow added, "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".
A tweet by Commons Speaker's wife Sally Bercow about Lord McAlpine was libellous the High Court in London ruled today.
Mr Justice Tugendhat will give his decision on the meaning of an allegedly libellous tweet she sent after a Newsnight report that wrongly implicated the Tory peer in child sex abuse allegations.
Earlier this month the judge reserved his decision in the case.
If the judgment goes in Lord McAlpine's favour, there will be another hearing at a later date on the appropriate level of damages, unless the two sides reach a settlement.
Mr Justice Tugendhat has reserved his decision to a later unspecified date in the Sally Bercow tweet case.
A tweet by Commons Speaker's wife Sally Bercow pointed "the finger of blame" at Tory peer Lord McAlpine during a media frenzy over allegations of child sex abuse, the High Court has been told.
Ms Bercow has always denied that the tweet was defamatory.
Sir Edward Garnier QC said it would be difficult to think of a more serious meaning than the one advanced by Lord McAlpine, who was not in court.
He told Mr Justice Tugendhat that his case was founded on the circumstances in which Mrs Bercow decided to tweet the peer's name - the media frenzy over a story that spread "like wildfire".
"The tweet, by itself, suggests that 'Lord McAlpine' has done something wrong. Drawing attention to someone and then adding the expression 'innocent face' hints at wrongdoing and negates any suggestion that the tweet was a neutral query to which the defendant was looking for an answer.
"The inclusion of the words 'innocent face' was giving a nudge and a wink to readers."
Mrs Bercow's counsel, William McCormick QC, told the judge that she promptly tweeted her apologies, provided letters apologising for the distress caused and making clear that the underlying allegations were untrue, and has offered to settle the case.
- Lord McAlpine was wrongly implicated by Newsnight on November 2, 2012, as being part of a paedophile ring which targeted children at a care home in Wrexham.
- His name was then widely mentioned on the internet, particularly Twitter.
- The former Tory politician reached a £185,000 settlement with the BBC for its botched investigation.
- He also received £125,000 from ITV and Phillip Schofield relating to a This Morning programme broadcast on November 8.
- Lord McAlpine is pursuing Sally Bercow, wife of Commons speaker John, over comments she made on the social networking site.
In February, Lord McAlpine, who has already received six-figure payouts from the BBC and ITV, announced that he was dropping defamation claims against Twitter users with fewer than 500 followers and instead asked for a charitable donation to BBC Children In Need.
The hearing before Mr Justice Tugendhat is only concerned with the actual meaning of the words complained of - both a natural and ordinary meaning and an innuendo meaning.
If the judge rules in Lord McAlpine's favour, there will be a hearing at a later date on the appropriate level of damages unless the two sides agree a settlement.
Commons Speaker's wife Sally Bercow will be at the High Court today for a hearing over her allegedly libellous tweet about Tory peer Lord McAlpine.
The former Conservative Party treasurer is seeking damages over a posting which he says meant that he was a paedophile who was guilty of sexually abusing boys living in care.
Mrs Bercow has always denied that her November 4 tweet, "Why is Lord McAlpine trending? Innocent face", was defamatory.
It followed a Newsnight report that wrongly implicated Lord McAlpine in child sex abuse allegations.