The incorrect claims against the Tory peer came about because of a botched Newsnight investigation.
Lord McAlpine said in a statement: "I am delighted to have reached a quick and early settlement with the BBC.
"I have been conscious that any settlement will be paid by the licence fee payers, and have taken that into account in reaching agreement with the BBC.
"We will now be continuing to seek settlements from other organisations that have published defamatory remarks and individuals who have used Twitter to defame me.”
A BBC statement said: "The settlement is comprehensive and reflects the gravity of the allegations that were wrongly made."
News of his settlement with the corporation comes after it emerged Sally Bercow would be the first person to receive a letter from his lawyers over her indirect reference to the false allegations on Twitter.
Lord McAlpine's solicitor Andrew Reid has urged anyone who named the peer on Twitter to come forward so they, too, can reach a settlement.
Mrs Bercow, the wife of House of Commons Speaker John Bercow, posted a tweet that referred to Lord McAlpine 'trending' on the social networking site.
Apparently responding to the revelation she would be contacted by lawyers, Mrs Bercow tweeted: "Thanks for phone calls/texts/tweets. I guess I'd better get some legal advice then. Still maintain was not a libellous tweet - just foolish."
Mr Reid had issued the warning to the hundreds of people thought to have defamed the peer.
"We know who you are," he said, adding specialist firms had recorded each offending post and the authors would be tracked down if necessary.
Lord McAlpine took legal action against the BBC after a Newsnight show led to him being mistakenly implicated in a paedophile ring that targeted a Welsh care home.
Although the show did not name the peer and only referred to a senior Conservative from the Thatcher era, it quickly led to him being identified online.
The fallout fuelled an existing crisis at the corporation sparked by the Jimmy Savile abuse allegations and led to the resignation of director-general George Entwistle.
Media watchdog Ofcom has now launched an investigation into both Newsnight and ITV's This Morning, which came under fire for ambushing David Cameron with a list of alleged paedophiles.
Earlier, Lord McAlpine spoke directly about the affair for the first time - and said it had left him devastated.
He pointed out that the whole situation could have been avoided if BBC investigators had called him before airing the claims.
The peer told BBC Radio 4's The World At One: "They should have called me and I would have told them exactly what they learned later on - that it was complete rubbish and that I had only ever been to Wrexham once in my life."
The peer admitted he felt the damage to his reputation was beyond repair because the cloud of suspicion would never completely disappear.
Paedophiles are "quite rightly figures of public hatred", he said, and added: "Suddenly to find yourself a figure of public hatred, unjustifiably, is terrifying."
An official report into the Newsnight programme, published this week, concluded staff had failed to complete "basic journalistic checks" ahead of the show on November 2.
Steve Messham, who claimed that a senior political figure of the time had abused him, was not shown a picture of the person he pinpointed and Lord McAlpine was given no right of reply.
There was also confusion about the chain of command and who had ultimate responsibility for signing off the show because editors had stepped aside in the wake of the Savile scandal.
After rampant speculation prompted the peer to issue an extraordinary statement protesting his innocence , Mr Messham was shown a picture and confirmed he had made a mistake.
Newsnight made a full, on air apology for the broadcast and hours later Mr Entwistle resigned. BBC director of news Helen Boaden and her deputy Stephen Mitchell have also now stepped aside while internal inquiries take their course.