Lord McAlpine, who was wrongly implicated in child sex abuse allegations, has settled his libel actions against the BBC and ITV for £310,000.
The former Tory Party treasurer was not at London's High Court to hear their solicitors apologise unreservedly for the damage and distress caused.
His lawyers confirmed the agreements involved the payment of £185,000 damages by the BBC and £125,000 from ITV, together with very substantial costs.
The peer's counsel, Edward Garnier QC, told Mr Justice Tugendhat the action followed a Newsnight broadcast in November.
The programme focused on the alleged sexual abuse of boys at the Bryn Estyn children's home in Wales in the 1970s and 1980s.
Two victims claimed they suffered abuse "at the hands of a leading Conservative politician from the Thatcher years".
The item did not name Lord McAlpine, but the programme-makers intended him to be the target of the allegations, he added.
"In short, Newsnight made the most serious of defamatory allegations about Lord McAlpine, tarring him as a paedophile who was guilty of sexually abusing vulnerable young boys living in care," he said.
Sir Edward said that six days after the Newsnight broadcast, ITV's This Morning included an interview with Prime Minister David Cameron.
During the interview presenter Phillip Schofield, referred to the Bryn Estyn scandal.
Schofield then passed Mr Cameron a card containing a list of names which were continually associated with the allegations that he said he had found on the internet.
Counsel said ITV and Schofield accepted that Lord McAlpine's name appeared on the list, which was briefly visible to viewers.
Solicitor David Attfield, for the BBC, said it withdrew the allegations unreservedly and apologised sincerely for the great damage and distress caused.
Mr Attfield said: "Following the broadcast of Newsnight on November 2, the BBC realised that it had committed a grave error in broadcasting the report complained of. The disgraceful allegations should never have been aired."
Ian Felstead, for ITV and Schofield, said they fully accepted and wanted publicly to state that there was no truth whatsoever in the allegations against Lord McAlpine.