A NEW biography on Billy Joel states that the first night the Piano Man got his soon to be wife Christie Brinkley to come back to his apartment, Elle MacPherson was already waiting for him.

In a new book, Billy Joel: The Definitive Biography, author Fred Schruers, who interviewed Joel for more than 100 hours for the book, tells of how the trio met in 1982 just after Joel’s split from first wife, Elizabeth Weber. It was first revealed in 2010 that Joel actually wrote the song Uptown Girl about MacPherson, and not Brinkley as it is widely thought.

The New York Post reports that Joel went to St. Bart’s for the holidays. He found a piano bar and began playing; a few moments later, to his wonderment, Macpherson, then just 19, and Brinkley, 28, were standing at either side of the 33-year-old — along with an undiscovered Whitney Houston.

They were all vying for Joel’s attention, Brinkley tells Schruers. “Whitney says, ‘I can sing!’ Meanwhile, Elle’s draped herself on the piano like Michelle Pfeiffer [in The Fabulous Baker Boys].”

Back in New York, Brinkley and Macpherson competed for Joel, who was living in a penthouse apartment overlooking Central Park. His doorman, a struggling actor named Nick Turturro, would rank all the women Joel brought home.

“Usually, he’d hold up eight, nine, 10 fingers,” Joel told Schruers. Brinkley was the only one to get 10 fingers twice.

The first night Joel got Brinkley to come home with him, “I was trying to act cool, but somewhere inside me the kid from Hicksville was going, ‘Yesssssss!’ ” When the elevator door opened to his apartment, there stood Macpherson. “Even as part of me thought, ‘Oh, God, no,’ another part of me was going, ‘Holy crap, if my friends could see me now.’ ”

Brinkley was unruffled. She left, Macpherson stayed, but Joel was in love with Brinkley. They married in 1985, and the album An Innocent Man was a love letter to her. They conceived their daughter, Alexa Ray, on their wedding night.

Yet Joel’s financial crises meant he had to tour non-stop to recoup his money, and the marriage suffered tremendously. The breaking point came in 1993. After a show at Nassau Coliseum, Joel opted to stay at a nearby hotel rather than make the 90-minute drive home, and Brinkley was told by one of Joel’s band members that he was having an affair. (Joel denies it.) By the end of that year, they knew the marriage was over — and it marked the last year Joel would issue a new album.

“Christie likes to joke that the end of the marriage ... spelled the end of my songwriting career,” Joel told Schruers. “At least, I think it’s a joke.”