The former president of New York-Presbyterian Hospital has finally admitted that an extramarital affair was the main reason for his hasty and mysterious departure from his $3 million-a-year job last fall.

Dr. Robert Kelly told hospital honchos in Florida that he left his old post in September to “work on’’ his 33-year marriage, adding the affair had not been with a hospital staff member, the Palm Beach Sun Sentinel reported.

He’s one of two finalists for the post of CEO of the Memorial Healthcare System, a hospital network based in Hollywood, Fla.

He told Memorial’s board that he had “personal family reasons” for quitting the high-profile New York gig.

The newspaper said he declined to discuss them because “I do feel like I need to protect my family.’’

A friend of both Kelly and his wife last month denied to The Post that Kelly had an affair.