The BBC and ITV have apologised to Lord McAlpine at the high court for "disastrously" and falsely linking him to allegations of child sex abuse.
Lawyers for the two broadcasters expressed "genuine remorse" and withdrew the allegations in a statement read by Sir Edward Garnier, counsel for McAlpine, on Tuesday.
The BBC and ITV have already agreed to pay the Tory peer damages of £185,000 and £125,000 plus legal costs respectively. McAlpine was not in court for a joint statement that concluded his action against the BBC and ITV.
McAlpine, the former Conservative party chairman, took action against the BBC over a bungled Newsnight report in early November that falsely linked him to an allegation of child sex abuse.
The following week, Phillip Schofield brandished a list of senior Tory politicians allegedly linked to child sex abuse live on air during ITV1's This Morning.
Garnier told the high court: "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.
"Those allegations are untrue. As the BBC now accepts, they were utterly baseless. These disgraceful allegations should never have been made."
Garnier, the former solicitor general, said McAlpine wished it to be known that he generally holds the BBC in great esteem. He added: "However, Newsnight broadcast the most highly defamatory allegations about him. Allegations which Lord McAlpine has said not only caused him great distress and embarrassment, but have affected him to his soul."
David Attfield, solicitor for the BBC, repeated the corporation's apology over the programme.
In a separate statement, Garnier addressed the ITV onscreen blunder which saw This Morning presenter Phillip Schofield reveal a list of senior politicians whose names he had found on the internet. He said ITV had accepted that McAlpine's name was on the list and that it was briefly visible to viewers during a live interview with the prime minister.
McAlpine's counsel said: "Notwithstanding that the allegations against him had finally to be shown to be false, Lord McAlpine understandably remained extremely hurt and distressed by the broadcast."
Ian Felstead, the solicitor representing ITV, apologised unreservedly to McAlpine, but said neither Schofield nor the broadcaster had intended to make the allegations.
Speaking outside court, McAlpine's solicitor, Andrew Reid, said the legal costs paid by the BBC and ITV amount to nearly £200,000 in total, on top of the damages payments amounting to £310,000.
Reid said that nearly 1,000 Twitter users had written to McAlpine to apologise for tweets that falsely linked him to allegations of child sex abuse.
The 2 November Newsnight story did not name McAlpine, but his name was widely linked to the report by Twitter users.
McAlpine is seeking £50,000 libel damages from one of the more high profile tweeters, Sally Bercow, the Commons speaker's wife.
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