La Russa is third on the all-time list with 2,728 wins as a manager. Cox is fourth at 2,504 and Torre fifth with 2,326. Only Connie Mack (3,731) and John McGraw (2,763) managed more wins.
"I am thrilled that these great managers during my tenure as commissioner will join the legends of our game in the halls of Cooperstown," MLB Commissioner Bud Selig said.
"In careers of consistent excellence and incredible longevity, Bobby, Tony and Joe all left indelible impacts on our national pastime. For decades, these three individuals not only led great ballclubs, but instilled in their teams a brand of class and professionalism that baseball fans admired.
"It is fitting that Bobby, Tony and Joe will share our game's highest honor together."
Cox managed the Toronto Blue Jays for four seasons and the Atlanta Braves for 25. He had a career .556 winning percentage and won five National League pennants and the 1995 World Series while leading the Braves.
La Russa had stints leading the Chicago White Sox (eight years), Oakland Athletics (10 seasons) and St. Louis Cardinals (16 years) and won 53.6 percent of the games in that span. He won six pennants and the 1989 World Series with Oakland and the World Series in 1989 with Oakland and 2006 and 2011 while with the Cardinals.
They are to be inducted into the Hall of Fame in Cooperstown, N.Y., July 28.
Other candidates on the Expansion Era Committee's ballot were players Dave Concepcion, Steve Garvey, Tommy John, Dave Parker, Dan Quisenberry and Ted Simmons; Manager Billy Martin; Marvin Miller, the first executive director of the Major League Baseball Players Association; and Yankees owner George Steinbrenner.
While Cox, La Russa and Torre were on all 16 of the committee's ballots, none of the other candidates received the 12 votes needed to gain indication.