Dave Dombrowski, who is the president of baseball operations for the Red Sox, and La Russa have been friends for nearly 40 years. La Russa began his 33-season managerial career with the Chicago White Sox in 1979 while Dombrowski worked as an administrative assistant in the organization.
The Red Sox said La Russa will assist Dombrowski in all areas of baseball operations, including player development and consultation with the major and minor league coaching staffs.
La Russa has spent the past four seasons in the Arizona Diamondbacks' front office. The 73-year-old announced last month that he would step down as the club's chief baseball analyst, and his contract with the Diamondbacks expired on Tuesday.
La Russa won the World Series in 1989 with the Oakland Athletics and in 2006 and 2011 with the St. Louis Cardinals. He retired from managing after the 2011 campaign and worked in the commissioner's office before joining Arizona's front office.
Elected to the National Baseball Hall of Fame in 2014, La Russa ranks third on Major League Baseball's all-time managerial wins list, having compiled a record of 2,728-2,365 (.536) from 1979-2011 with the White Sox (1979-86), Athletics (1986-95), and Cardinals (1996-2011).