Spokeswoman Claire Mercuri said the 53-year-old had left the Silver Hill Hospital in Connecticut on Wednesday and was now back at home.

The Grammy award-winning pianist and singer entered the clinic last week with what Ms Mercuri called "a specific and personal problem that had recently developed".

I began what was a prolonged period of overindulgence - I don't want to get more specific

Billy Joel

The star told People magazine that he underwent treatment as a Father's Day gift to Alexa, his 16-year-old daughter by his ex-wife, model Christie Brinkley.

"I told my daughter that I recognised I was having a problem. And my gift to her for Father's Day was going to be cleaning up my act," he said.

Ms Mercuri said Joel had now returned to his home in Long Island, New York.

"He's feeling well," she said.

There has been speculation about Joel¿s health since March, when he rescheduled part of a tour with Elton John.

At the time, his tour manager was reported as saying that he was suffering from acute upper respiratory infection and laryngitis.

Joel was married to model Christie Brinkley

At a March concert at New York's Madison Square Garden, the singer slurred his words and nearly fell asleep, according to the New York Daily News.

The paper also said that Joel had cancelled an appearance at a Songwriters Hall of Fame dinner in New York after crashing his Mercedes.

Joel, whose hits include 52nd Street and Uptown Girl, has suggested his problems were triggered by a bout of depression after pulling out of the tour.

"I took this very hard," he said.

"I then began what was a prolonged period of overindulgence. I don't want to get more specific."

The piano-playing singer, who is divorced from model Christie Brinkley, is known for a long series of hits which started with the album Piano Man in 1974.

His hit singles have included Just the Way You Are, My Life, Tell Her About It and Uptown Girl.

The songwriter's most recent album, Fantasies and Delusions, was a classical work featuring pianist Richard Joo.