Hartnett, 30, who is appearing in the West End in a production of Rain Man, is to donate the money to a variety of charities.
Mr Justice Eady, sitting at the High Court in London, was told that the action concerned an article published in the Daily Mirror on 1 September entitled "Josh Hartnett's saucy CCTV romp".
The star's Graham Atkins Solicitor said: "The article alleged that the claimant 'took a mystery lady' to the Soho Hotel in London and that 'their steamy shenanigans were caught on CCTV'."
He added: "It further alleged that 'dumbstruck' and 'cringing hotel workers saw all of Josh's X-rated moves' which resulted in the Soho Hotel asking the claimant 'to take his personal business elsewhere in the future'."
Mr Atkins said the defendant, MGN Ltd, publisher of the Daily Mirror, accepted that the allegaations "are entirely false".
Mr Atkins said: "The incident never happened and accordingly the Soho Hotel has never asked the claimant to 'take his personal business elsewhere in the future'.
"Indeed, the claimant remains a welcome guest there."
The lawyer told the judge: "The publication of this false article has caused hurt, embarrassment and distress to the claimant.
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