Lord McAlpine has reached a £125,000 settlement with ITV and Phillip Schofield over an edition of This Morning.
In a statement, ITV said: "ITV and Phillip Schofield have now reached agreement with Lord McAlpine to settle his libel claim over the This Morning programme broadcast on November 8.
"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. Ofcom has launched an investigation into the incident, while ITV said 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 him and 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's solicitor Andrew Reid told BBC Radio 4's The World At One: "We reached a settlement with ITV of £125,000 damages - not an insubstantial amount. My client is pleased with that amount of money.
"It is a pragmatic settlement. I think we accepted the legal argument that the Newsnight programme had effectively set the pot boiling at that point and the Schofield stunt added fuel to the fire that was already there, and we had to take that into account. It was listening to sensible legal argument."
Asked whether Lord McAlpine would be ready to accept an apology from those who named him online, Mr Reid said: "No. There will be damages paid, and costs." He said he had already received "a huge amount of emails" from Twitter users, which have now been processed.
Mr Reid added: "Don't forget that the software we have enables us to look at all the social media, so we are not going to be looking just at Twitter. If there are any people who think our search is just going to be confined to Twitter, it is not. Please come forward - it is much easier."