The 29-year-old Lester, who has spent his entire eight-year career in Boston, just completed the final year of a five-year, $30 million contract that had a team option for the 2014 season.
The Red Sox had until midnight ET Saturday to pick up the option.
Lester was 15-8 with a 3.75 ERA in the regular season, and led the team in games started (33), innings pitched (213 1/3), strikeouts (177) and quality starts (20).
He was 4-1 during Boston's run to the World Series title, winning both his starts in Games 1 and 5 against the St. Louis Cardinals. Lester allowed only one run and nine hits in 15 1/3 innings in those starts, and his 0.59 ERA was the best by a Red Sox pitcher making multiple starts in a World Series since Hugh Bedient in 1912 (0.50).
Lester, who was selected by the Red Sox in the second round of the 2002 draft, has a 100-56 record with a 3.76 ERA in 221 career regular-season appearances. His 1,237 career strikeouts are the most ever by a Red Sox left-hander.