Girardi, a former Yankee player, will be the 32nd manager in franchise history.
"I can't tell you how honored we are to be putting on this uniform for the third time," the 43-year-old Girardi said at a news conference at Yankee Stadium. "This is the place to be. For the Girardis, this place is home."
Reports have said he will be paid $8 million annually over three years.
The former Florida Marlins skipper will be the 17th Yankees manager to also have played for the club and the fourth former Yankees catcher to manage the team, joining Bill Dickey, Ralph Houk and Yogi Berra.
He will be the major league's third-youngest manager behind the Washington's Manny Acta (38) and the Cleveland Indians' Eric Wedge (39).
He played on the Yankees' 1996 World Series champions, and in 2005, served as Torre's bench coach and catching instructor.
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