Farrell has never managed at any level. He succeeds Cito Gaston, who retired after the season.
Farrell will be introduced at an afternoon news conference. On Sunday, Red Sox owner John Henry said in an e-mail to the Boston Globe that Farrell would be going to Toronto.
The 48-year-old Farrell was Cleveland's player development director for five years and Boston's pitching coach the past four seasons. He pitched in the majors for parts of eight seasons with Cleveland, California and Detroit. His final season was 1996.