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".
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.
Reid said: "We have had to deal with the two large actions, which is the BBC and ITV. We are starting to move now to the large-scale tweeters.
"We have now heard from Bercow's solicitors and no doubt progress will be made there in due course."
Asked whether Lord McAlpine would be ready to accept an apology from those who named him online, 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.
"We have got a website up where people can get on, fill in the form and then we will come back to them once we have set the amount of money we are going to ask them to pay us for us to forward on to BBC Children in Need."
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."
Asked what explanation the tweeters were giving for naming Lord McAlpine online, Reid said: "Most of them seemed to have this idea that Twitter was like their kitchen table or a coffee morning. They just didn't think that the ordinary laws that apply to defamation applied to Twitter.
"All of them said `We are really sorry, we just didn't realise what we were doing and we didn't realise the effect of the proliferation of tweets…'.
"It is correct that we have met with senior officers from Scotland Yard and what we have discussed with them is very simply this: there are a hardcore of people who are retweeting and who are basically acting maliciously and this is an offence.
"No doubt in due course they will investigate that, or not. That's up to the police, not up to ourselves."
Reid said Lord McAlpine had given him no indication that he wants to wind up his action before tracking down and dealing with all those who named him online.
"I am not running a crusade or a campaign," he said. "I take my instructions from Lord McAlpine and he will tell me when he wants to end this taking of apologies, or for that matter dealing with people via legal proceedings. At this moment in time, I have not received instructions to desist."
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