Sir Elton John and David Furnish have accepted "significant" libel damages over a newspaper allegation that their dog inflicted "Freddy Krueger-like" injuries on a child at a play date.
The couple brought proceedings against News Group Newspapers over a front page story in The Sun on Sunday in February.
Their solicitor said the injuries were not serious and that the allegation was "false and seriously defamatory".
Neither Sir Elton nor Furnish was at London's High Court on Friday.
The Sun's story, captioned Elton's Dog Did This To My Girl, reported that Sir Elton's spaniel bit a five-year-old girl at the singer's Berkshire home in February 2016.
Solicitor Jenny Afia said the story had claimed the child had been "subjected to a serious attack" and that Sir Elton and Furnish had "failed to make any attempt to find out how the little girl was... despite being aware of the incident."
"The truth is that the injuries were not serious, and the claimants, far from ignoring the incident, made several inquiries about the girl's welfare to her father and nanny," Mr Justice Matthew Nicklin was told.
"Each time it was confirmed the girl was fine.
"I am pleased to say that the newspaper has now accepted unequivocally that this allegation was false and seriously defamatory.
"As a result, it has agreed now to apologise to Sir Elton John and David Furnish, and to pay significant damages as well as to reimburse their legal costs."
"The defendant offers its apology to the claimants and is pleased that the matter has been amicably resolved," said Jeffrey Smele, solicitor for News Group Newspapers.
The Sun on Sunday's story appeared on the paper's website and was picked up by a number of other publishers, including Metro, the Daily Mirror and the London Evening Standard.
Sir Elton John and David Furnish married in 2014 and have two children - seven-year-old Zachary and Elijah, aged five.
David Furnish and Sir Elton John with their sons Elijah and Zachary