"The settlement is comprehensive and reflects the gravity of the allegations that were wrongly made."
The statement confirmed that Alistair McAlpine, who was appointed Conservative Party treasurer under Margaret Thatcher, would receive £185,000 ($294,000) plus costs and that a statement would be read in court to apologise for the allegations.
McAlpine responded: "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."
The broadcaster has already apologised for a report broadcast by its flagship current affairs programme Newsnight about abuse at a children's home in Wrexham in Wales in the 1970s.
The report did not name him but he was quickly identified on social networking sites.
The false allegations, coming as the BBC was under intense scrutiny over its decision to spike a report about child abuse claims surrounding late presenter Jimmy Savile, plunged the world's largest broadcaster into one of the worst crises in its history.