Martin O'Neill has won "substantial" damages from the BBC over claims that he "exploited the loose disciplines of football" over transfer deals.
Mr O'Neill sued the BBC over the allegations
The allegation was made in publicity for a book published by BBC Worldwide, which said the Celtic manager had shares in a football agent business.
One of the authors said he had dealt in its players while a shareholder.
At the High Court in London, the BBC accepted this was untrue and apologised for the claims in the press release.
Mr O'Neill's solicitor Paul Hackney said his client had agreed to accept a formal apology and "substantial damages" from the BBC and Richard McIlroy.
He was one of the authors of the book Football Confidential 2, a follow-up to a series of programmes on Radio Five Live entitled On the Line.
The Celtic manager took legal action over claims made in the book and publicity for the publication.
The book named him as one of 10 managers with shares in the ProActive Sports Group, which represents a number of high-profile players.
It claimed that this might give rise to a potential conflict of interest were a manager to buy or sell a player represented by the company.
It also alleged that Mr O'Neill's lawyers had tried to suppress the release of the information about his shareholding.
Mr McIlroy gave an interview claiming that the Celtic manager had "dealt in" players represented by ProActive while he was a shareholder.
A press release issued by the BBC suggested that he had "exploited the loose disciplines of football" through his shareholding.
Alex Marzec, counsel for the BBC, said: "The defendants accept that the claimant did not buy or sell players who were represented by ProActive whilst he was a shareholder in that company.
"BBC Worldwide and Mr McIlroy also accept that Mr O'Neill behaved reasonably in contacting his lawyers to ensure the accuracy of what was broadcast.
Conflicts of interest
"The defendants apologise to the claimant if contrary impressions were given."
The BBC also apologised for the statement in the press release, which the corporation accepted was untrue.
Mr Hackney said: "Martin O'Neill is very pleased that he has been able to clear his name.
"While he understands that the media have a duty to investigate potential conflicts of interest, it has always been his case that he was unfairly singled out by the On the Line team, both at the time of the Radio Five broadcast in 2002 and especially in the book of the series published last year."