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.
Former Conservative minister Lord Tebbit said Lord McAlpine, who has died aged 71, was "deeply upset" by the recent incorrect allegations about his private life.
Lord Tebbit told the BBC: "He had always got something interesting to say. A very cultured man, very interested in the arts, also much-travelled.
"He seemed to find a quite natural home in Italy in recent years."
Lord McAlpine was falsely implicated in abuse allegations following a BBC Newsnight investigation.
Lord McAlpine was a "man of integrity" who made a huge contribution to public life, Conservative Party chairman Grant Shapps has said.
The former deputy Conservative Party deputy chairman died last night in Italy at the age of 71.
"Lord McAlpine made a huge contribution to public life," Mr Shapps said.
"He was a man of integrity who had a successful career in both politics and business.
"He was a towering figure during the Thatcher era who did much for the Conservative Party and our country.
"My thoughts are with his friends and family."
David Cameron has paid tribute to Lord McAlpine who has died at the age of 71.
My thoughts are with Lord McAlpine's family - he was a dedicated supporter of Margaret Thatcher and the Conservative party.
The former Conservative Party deputy chairman died last night in Italy, his family confirmed.
Former Conservative Party deputy chairman Lord McAlpine has died aged 71, his family has announced.
Lord McAlpine, who was previously an aide to Prime Minister Margaret Thatcher, died last night in Italy, his family said.
They said in a statement, "It is with great sadness that the family of Lord McAlpine announce his peaceful death last night at his home in Italy."
Former Conservative Party deputy chairman Lord McAlpine has died, his family has announced.
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.