Cox ended a 25-season tenure as the Braves' manager Monday when Atlanta was eliminated from the National League playoffs by the San Francisco Giants.
Gonzalez, 46, was the manager of the Florida Marlins from the beginning of the 2007 season until June 23 when he was fired. The Marlins were 87-75 under Gonzalez, who previously spent time on Cox's staff as a third base coach.
Cox, 69, had a 2,149-1,709 record as the Atlanta manager. He led the Braves from 1978-1981 and again from 1990-2010. Cox also had a four-season stint as the manager of the Toronto Blue Jays.
He won five National League pennants and the 1995 World Series championship. The Braves finished first in their division 14 times under Cox. His total 2,504 wins is fourth highest in major-league history.
"I don't know if I've had an imprint [on the organization]," Cox said Wednesday at his farewell press conference. "The team and organization has established itself as a high-end organization. We want to maintain that for sure. I think a lot of organizations have patterned themselves after the way we've built things here."