Beckham sued MGN Ltd, owners of The People over a July 10 article headlined "Beckham's Hate Calls to Nanny".
The story claimed Beckham had been plaguing ex-nanny Abbie Gibson with abusive messages since she quit her job four months earlier.
At a brief hearing at London's High Court, Beckham's lawyer Gerrard Tyrrell told the judge MGN had apologised for the story and agreed to pay damages to Beckham.
"These allegations are completely untrue. David Beckham has not made any telephone call of the sort described in the article, nor indeed has he spoken to Ms Gibson since she resigned her employment in April 2005," Tyrrell said.
"The defendants acknowledge that David Beckham did not behave in the manner reported and that the article was incorrect. The defendants also accept that the quotes attributed to a supposed 'Beckham family source' had nothing to do with either David Beckham or his wife," Beckham's lawyer told the court.
"The defendants have apologised to David Beckham. They have also agreed to pay to him substantial damages together with his legal costs and have agreed to undertake not to repeat the defamatory allegations."
Rachel Glavin, lawyer for MGN, said: "The defendants acknowledge that the allegations made against Mr Beckham and acknowledged by Abbie Gibson were untrue and are happy to give the undertaking. The defendants apologise for the distress and injury caused to him."