Lord McAlpine has reached a £125,000 settlement with ITV and Phillip Schofield over a This Morning programme on 8 November.
In a statement, ITV said: "ITV and Phillip Schofield have now reached agreement with Lord McAlpine to settle his libel claim, made in relation to the This Morning programme broadcast on November 8 2012.
"ITV and Phillip Schofield apologise unreservedly to Lord McAlpine, have agreed the terms of a statement to be made in open court, and have agreed to pay him damages of £125,000 and his legal costs."
The broadcaster sparked fury after This Morning presenter Schofield brandished a list of names of alleged abusers that he had found on the internet and handed it to the Prime Minister during a live interview, asking if he would investigate them.
Ofcom has also launched an investigation into the incident, while ITV said that disciplinary action had been taken.
ITV is the second name in a long list of organisations and individuals pursued by Lord McAlpine for wrongly linking him to a paedophile ring.
Action is being considered against a "very long list" of Twitter users who wrongly named the former Tory politician, thought to include comedian Alan Davies and the Commons Speaker's wife Sally Bercow.
And it emerged yesterday that police are starting a "scoping process" to look into whether any criminal offence has been committed.
Lord McAlpine has asked those who linked him to child abuse allegations to apologise formally and pay a "sensible and modest amount", which he plans to donate to BBC Children in Need.
Lawyers for the peer reached a £185,000 settlement with the BBC last week after it broadcast a botched Newsnight investigation into child abuse at a North Wales care home.
Lord McAlpine was mistakenly implicated by Newsnight's November 2 broadcast in a paedophile ring that targeted children at the care home in Wrexham.
The peer said the damage of the Newsnight report "can't be repaired" and he now has to live with the legacy of suspicion.
After the broadcast, Newsnight carried a full, on-air apology for the broadcast a week later.
An official report by the BBC's Scotland director Ken MacQuarrie into the botched investigation concluded that Newsnight staff had failed to complete "basic journalistic checks".
Mr MacQuarrie also found there was confusion about who had responsibility for "final editorial sign-off", adding that the programme's editorial management structure had been "seriously weakened" as a result of the editor having to step aside over the Jimmy Savile scandal, and the departure of the deputy editor.
Disciplinary action is being pursued over the incident.
Lord McAlpine has said the BBC could have saved "a lot of agonising and money" by simply calling him before the programme went out.