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The settlement came as media reports said one of the BBC's former stars had been arrested as part of an ongoing police investigation into sex crimes centred on the publicly funded broadcaster.
Lord Alistair McAlpine, an ally of former Prime Minister Margaret Thatcher, was widely named on the internet as being the unidentified senior politician accused in a report by the BBC's flagship Newsnight programme of abusing boys in social care.
The flawed film sparked one of the worst crises in the broadcaster's 90-year history and claimed the scalp of Director General George Entwistle, after the abuse victim central to the BBC investigation said McAlpine was not one of his attackers.
"I am delighted to have reached a quick and early settlement with the BBC," McAlpine said in a statement.
"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."
His lawyer warned others who had sullied his client's reputation to get in touch before they too faced litigation, a threat which could ensnare hundreds of Twitter users and bloggers who wrongly named McAlpine.
"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," McAlpine said.
TWITTER USERS IN THE FRAME
One of the first who could face action is Sally Bercow, the flamboyant wife of Britain's parliamentary speaker who keeps lawmakers in order during debates.
She had tweeted: "Why is Lord McAlpine trending? *innocent face*" as speculation mounted after the Newsnight report. On Thursday, she wrote: "I'm getting legal advice. Shocked that I'm first person Lord McAlpine coming after though."
The controversy convulsed the national broadcaster just as it was trying to grapple with revelations that a former star presenter, Jimmy Savile, who died last year aged 84, was one of Britain's most prolific sex offenders.
Police investigating claims against Savile, said on Thursday they had arrested a fourth man, aged in his 60s, on suspicion of sexual offences and added the number of victims who had come forward with allegations had now risen to 450.
The BBC and other media named the arrested man as radio presenter Dave Lee Travis, who once appeared on the same TV show and radio station as Savile and whose radio show Myanmar's opposition leader Aung San Suu Kyi said had provided her with comfort during her many years in captivity.
A Reuters photographer reported there were a number of police officers outside the home of Travis, 67, a short distance north of London. Travis publicly denied any allegations of impropriety when claims first surfaced last month.
The BBC's much-criticised handling of the Savile allegations and the mistaken child abuse report on Newsnight prompted BBC Trust Chairman Chris Patten to warn that the world's biggest broadcaster was doomed unless it reformed.
Patten, a former Conservative minister who is best known for handing back Hong Kong to China in 1997, was due to meet the 11 other BBC trustees on Thursday to try to plot a way out of the crisis and find a successor to Entwistle, who quit on Saturday.
McAlpine, who is 70 and in poor health, said in a BBC interview it had been a "horrendous shock" to find out that he was being linked to a claims of a high-level paedophile ring.
He said the BBC should have called him about the allegations before airing the report.
"They could have saved themselves a lot of agonising and money, actually, if they'd just made that telephone call," McAlpine said. "I would have told them exactly what they learnt later on ... That it was complete rubbish."
At the height of the frenzy following the Newsnight show on Nov. 2, a presenter on a chat show on the ITV channel brandished a list of alleged abusers during an interview with Prime Minister David Cameron.
Britain's media regulator said it was investigating both the Newsnight report and ITV, which said it too had received a letter from McAlpine's legal team.
Peter Fincham, ITV's Director of Television, said what his channel's show had done was "wrong" and "misguided", and that "appropriate" disciplinary action had been taken.
The regulator, Ofcom, could theoretically fine ITV a maximum of up to 5 percent of annual turnover while the maximum fine for the BBC, not an Ofcom licensee, would be 250,000 pounds.
Other penalties open to Ofcom are directing the broadcasters not to repeat the allegation, or to issue a correction.