Lord McAlpine, 71, was previously an aide to Prime Minister Margaret Thatcher.
He died last night in Italy, his family said.
In a statement, they said: "It is with great sadness that the family of Lord McAlpine announce his peaceful death last night at his home in Italy."
Prime Minister David Cameron said Lord McAlpine was a "dedicated supporter of Margaret Thatcher and the Conservative party".
Colleagues described him as a "towering figure" who made "a huge contribution to public life".
But the former Conservative Party deputy chairman, previously an aide to prime minister Margaret Thatcher, was more recently wrongly implicated in a child abuse scandal.
Leading the tributes, Mr Cameron said on Twitter: "My thoughts are with Lord McAlpine's family - he was a dedicated supporter of Margaret Thatcher and the Conservative party."
In a statement, the family of Lord McAlpine, Baron of West Green, said: "It is with great sadness that the family of Lord McAlpine announce his peaceful death last night at his home in Italy."
A former political adviser and businessman, Lord McAlpine was more recently in the news when he received damages from a string of internet users - including Sally Bercow, wife of Commons Speaker John Bercow, and comedian Alan Davies - as a result of libellous messages on Twitter.
Ms Bercow agreed to pay Lord McAlpine £15,000 in damages for her infamous "innocent face" tweet, which was posted at the height of the allegations into child sex allegations and the Tory peer.
Actor Davies also paid damages after he ''re-tweeted'' a Twitter post which linked Lord McAlpine's name to a television report about a ''senior political figure who is a paedophile''.
Lord McAlpine was wrongly implicated in a child abuse scandal when allegations about a senior Tory were the subject of a BBC Newsnight investigation.
The BBC was later forced to apologise and issued a statement after abuse victim Steve Messham admitted that the man who abused him in a North Wales children's home in the 1970s and 1980s was not the peer.
Solicitors for Lord McAlpine indicated that they were preparing to sue for defamation, saying their client's reputation had been left in ''tatters'' as a result of the programme.
An investigation into the programme by the BBC Trust later said members of the team failed to follow the corporation's own editorial guidelines.
The allegations forced the corporation's then-director general, George Entwistle, to quit the role in November 2012 less than two months into taking it, saying that as editor-in chief he had to take ''ultimate responsibility'' for a Newsnight investigation that had led to Lord McAlpine being wrongly accused of child abuse.
Friends and colleagues today paid tribute to Lord McAlpine.
Conservative Party chairman Grant Shapps said: "Lord McAlpine made a huge contribution to public life.
"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."
Conservative former chairman and Cabinet minister Lord Parkinson, who worked closely with Lord McAlpine during the Thatcher era, said: "Alistair McAlpine was an outstanding treasurer of the modern Conservative Party - if not the outstanding treasurer.
"He served as treasurer when deputy chairman during the whole of the Thatcher years and was an extremely successful fundraiser. He was also a very close adviser to Mrs Thatcher and had her total trust. In addition to all these things he was a most unusual, intriguing, interesting character with a fantastic range of interests."
The Tory former minister Lord Tebbit said the late peer was a "confidante" to Lady Thatcher, but was "deeply upset" by the recent 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."
Of the wrongful allegations, Lord Tebbit said: "I think he was pretty upset about it, deeply upset, that anybody would for a moment believe that of him.
"It centred around a faintly ridiculous idea that Alistair had some role in organising a gay sex scandal - well it would have been if it had existed - at Number 10 Downing Street. You only have to ask yourself about what Denis Thatcher would have said about such a proposal to realise it was totally absurd."