A High Court judge ruled that a tweet written by Sally Bercow about Lord McAlpine was libellous.
A failure to follow editorial guidelines led to Newsnight's infamous report that saw Lord McAlpine later falsely exposed as a paedophile.
Lord McAlpine will receive a payment of £185,000 after a settlement was reached with the BBC over false claims made in a Newsnight report.
Comedian Alan Davies has paid damages to the former Tory deputy chairman Lord McAlpine after he retweeted a libellous tweet.
The offending tweet falsely implicating the peer in allegations of child sex abuse.
Davies apologised for the "great damage and distress" his tweeting caused.
Neither Lord McAlpine nor Davies was at the High Court in London for today's hearing and lawyers did not reveal how much Davies paid.
Davies hoped that other Twitter users would be more aware of the "potential damaging consequences of tweeting," a lawyer representing the comedian said.
Lord McAlpine's libel action against the House of Commons Speaker's wife Sally Bercow has been formally settled at the High Court.
Lord McAlpine's QC, Sir Edward Garnier, told the judge that Mrs Bercow had apologised for her "irresponsible use of Twitter" following a report that falsely implicated the Conservative peer in abuse allegations.
She accepted an offer to settle the matter in May after Mr Justice Tugendhat ruled that the tweet in question was highly defamatory.
Mrs Bercow's QC, William McCormick, said today: "Mrs Bercow wishes and hopes that as a result of this matter other Twitter users will behave more responsibly in how they use that platform. She certainly intends to do so herself."
He added that should Mrs Bercow reactivate her Twitter account, it is now a legal requirement that she must formally issue her apology on it.
Lord McAlpine's lawyer said Sally Bercow "must now accept" that her tweet about the Conservative peer was defamatory after the High Court ruled it was libellous.
Andrew Reid of RMPI Solicitors said:
The apologies previously received from Mrs Bercow did not concede that her tweet was defamatory. Clearly she must now accept this fact.
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.
Mr Justice Tugendhat's judgement is one of great public interest and provides both a warning to, and guidance for, people who use social media.
The High Court judge who ruled a tweet by Sally Bercow about Lord McAlpine was libellous said her followers - who numbered 56,000 - would likely know by the time of her post the elements of the story told on Newsnight.
"In my judgement, the reasonable reader would understand the words 'innocent face' as being insincere and ironical", Mr Justice Tugendhat said.
"There is no sensible reason for including those words in the tweet if they are to be taken as meaning that the defendant simply wants to know the answer to a factual question".
The reader would reasonably infer that Mrs Bercow had provided "the last piece in the jigsaw".
Her tweet, by implication, was a repetition of the accusation with the addition of the name which had previously been omitted.
"It is an allegation of guilt. I see no room on these facts for any less serious meaning", the judge said.
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.
– A statement by Sally Bercow
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.