NEW YORK — Howard Stern once worried on the air that a marriage to longtime girlfriend Beth Ostrosky would only mess up a good thing. It seems he’s willing to take the risk.

Stern announced on his satellite radio show on Wednesday that he had proposed the evening before — and Ostrosky had said yes.

Stern told listeners that he surprised the model with an engagement ring while they were naked in bed.

”Are you for real?” he said she responded.

It’s a turnaround for the media maverick, who launched his satellite radio show last year with comments that he was happy to leave things as they were.

”I am not married,” Stern said then. ”It’s a nice feeling that we get along great. We’re very happy, and I don’t want to (mess) it up.”

Stern has been married before. He bragged of his marital fidelity while entertaining scores of strippers and porn stars on his previous radio show before splitting from his wife of 21 years in 1999.

Stern and his ex-wife, Alison Berns, whose romance was the basis of his film ”Private Parts,” have three daughters. They divorced in 2001.