Chegwin, who fronted a naked gameshow 'Naked Jungle' on the then Channel 5 two years ago, brought the High Court libel case against the Trinity Mirror title after the Sunday paper ran a front page story in January.
The paper has apologised and agreed to pay a "substantial" sum in damages.
The paper ran the story, despite an undercover reporter being unable to find any evidence that Chegwin had tried to bribe a police officer for a new TV show reuniting C-list celebrities with their first cars.
The paper had said that Chegwin planned to gain access to the Police National Computer to get access to confidential details of cars once owned by celebrities for a programme called 'Stars and Their Cars'.
In a statement, lawyers acting for Chegwin said: "In a sudden climbdown, lawyers acting for The People have agreed that the story was without foundation and to apologise for the article and pay damages to Keith Chegwin for publishing such a serious libel."
David Price, Chegwin's solicitor, said the editor at the time Neil Wallis and publishers Trinity Mirror accepted that the TV presenter, who once worked on children's morning show 'Swap Shop' and went on to front pop show 'Chegger's Plays Pop', had not attempted to break the law nor had he hatched a plan to do so.
Price said what had happened was that Chegwin's agent approached a private detective agency for help in research for the pilot show.
However, an undercover People reporter posing as a detective from that agency, contacted Chegwin and asked whether he would pay cash to a police officer, which Chegwin, on secret recordings, said not to.
"Throughout, the reporter recorded their conversations using covert audio and video recording equipment. Mr Chegwin, who never had any intention of bribing anyone, refused to allow money to be offered to a police officer to access the PNC for the programme," Price said.
The newspaper also alleged that Chegwin allowed for cut-price drinks to be made available at an Edinburgh club when he previously won public sympathy for his alcoholism, which led to the break-up of his marriage to Maggie Philbin.
The People accepted that this was never the case and agreed that the nightclub had no connection with the TV presenter and was not endorsed by him.
Wallis has since been replaced at The People by Mark Thomas. Wallis left for News of the World where he has been appointed deputy editor. Thomas, former deputy editor of The Sunday Mirror, has also worked at the News of the World and The Daily Mirror. Alan Edwards, deputy editor of The People, has been acting editor since the start of the year.
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