Paul McCartney: Engaged to Nancy Shevell!

Sir Paul McCartney and New York businesswoman Nancy Shevell are engaged after four years together.

“They have the right chemistry,” a source tells People. “They’re both cool, chilled out and optimistic.”

FYI: This will be Paul‘s third marriage: He married Linda McCartney in 1969 and Heather Mills in 2002. Paul has five children: Heather, 48, Mary, 41, Stella, 39, James, 33, and Beatrice, 7.

The Beatles legend, 68, and Nancy, 51, started dating Summer 2007 in the Hamptons. Pictured here is the couple at the MET Ball on Monday (May 2).