Cox managed the Atlanta Braves and both Torre and LaRussa played for the team.
Each of the inductees won more than 2,000 games in managerial careers that spanned more than four decades. Cox led Atlanta to one championship and 14 straight division titles. Torre became the fifth manager to win at least four World Series titles. La Russa won championships with Oakland and St. Louis.
The announcement was made Monday at the winter meetings. They will be inducted July 27 in Cooperstown, N.Y., along with any players chosen by the Baseball Writers’ Association of America.
Greg Maddux and Tom Glavine, 300-game winners, are among the newcomers to the writers’ ballot, with results announced Jan. 8.