The deal came after Walsh, best known for his role as a judge on the hit television show "The X Factor", sued the group for publishing a story last year based on false allegations that he had groped a man in a Dublin night club.
Leonard Watters, who made the accusations before later retracting them, was jailed for six months earlier this year.
Paul Tweed, Walsh's solicitor, said: "The publishers of the Irish, UK and online editions of the Sun have this morning unreservedly apologized to Louis Walsh.
"They have also agreed to pay very substantial damages of 500,000 euros together with his legal costs."
Walsh, who managed Irish boy bands Westlife and Boyzone, said the story had a "terrible effect" on him.
"I'm very satisfied with this morning's total vindication for me, but I remain very angry at the treatment I received at the hands of the Sun," he said outside court.
"I have the utmost respect and time for most journalists with whom I've always enjoyed a good relationship, and I'm therefore absolutely gutted and traumatized that these allegations should have been published
"I wouldn't wish this on my worst enemy."
The Sun said it apologized "unreservedly".
(Reporting by Sarah O'Connor)
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