Billy Joel -- MOVIN' OUT ... Sells Miami Mega-Mansion

Billy Joel has parted ways with his enormous Miami mansion, TMZ has learned -- and the guy who bought it from him is a mega-mega-rich fashion mogul.

Sources close to the deal tell us, the sale went through Friday for just under $14 million. The 7-bedroom, 8.5-bath waterfront super house has been on the market since May 2012, when Billy listed the home for $14.75 million.

And the mystery buyer -- a guy named Diego Della Valle ... owner of Tod's shoes and majority shareholder in Saks Fifth Avenue. He's worth a reported $1.55 BILLION ... nearly ten times what Billy's reportedly worth ($160 million).

Billy bought the place for $13.5 million in 2006 -- but after he pays the agents' commissions, we're told the singer will actually have lost money on the deal.