Costner, whose films include Robin Hood: Prince of Thieves and Dances With Wolves, was accused by a masseuse at the Old Course Hotel, in St Andrews, of carrying out a sex act on himself after removing his towel.
The 34-year-old masseuse claimed that she was unfairly dismissed after complaining to hotel managers about the behaviour of the actor.
Costner, 51, was on honeymoon with his wife, Christine Baumgartner. The couple were staying at the hotel while attending the Dunhill Links pro-celebrity golf tournament.
A hearing into the spa worker's claims of unfair dismissal and sexual discrimination was due to resume when lawyers revealed that a private settlement had been reached.
Details of the agreement were not revealed and the masseuse, who cannot be named for legal reasons, refused to comment as she left the tribunal in Dundee.
Last month she said the alleged incident happened while she was giving Costner a massage in October 2004. She said: "I asked him how he liked his massage and he said he liked it sweet. I thought it a strange term to describe a massage.
"He asked me if I was comfortable touching him everywhere and I said no. Throughout the massage he kept putting his hand underneath his towel but he never kept it there long enough for me to suspect anything."
She said he then removed the towel, grabbed her wrist and performed a sex act.
"It was disgusting," she told the hearing.
"Even though he was a Hollywood superstar, I could not believe he thought he could get away with something like that.
"When I was giving his wife a massage afterwards, I wanted to tell her everything."
The masseuse complained that the hotel failed to provide her with adequate counselling. She claimed that after the alleged incident, which happened as new American owners were taking over the hotel, she was blamed for everything that went wrong in the spa, including two small fires, and was sacked last August. Nicol Hosie, the tribunal chairman, ruled that there was no longer a strong enough case to justify withholding Costner's name.
He added that it was unlikely that Costner was unaware of the allegations against him, given the coverage the story had received in the American press and on the internet.
Solicitors for Costner in America said after the story was first published: "We find it unfortunate that Mr Costner's name is being brought into what is essentially a dispute between a company owned by a good friend of his and a former employee and that it would tarnish what was a wonderful time spent at this resort with his wife."
Paul Bloch, a spokesman for Costner, said last night: "This was never about Kevin. It is a dispute between a hotel and an employee. It is nothing to do with Kevin Costner."
