The right-hander will receive $14.5 million in each of the next two seasons. Peavy could receive a $15 million option for 2015, depending on innings during the next two years.
Peavy's previous deal included a $22 million option for next season with a $4 million buyout. The buyout will be paid in equal installments from 2016-19.
The 2007 NL Cy Young Award winner went 11-12 with a 3.37 ERA in 32 starts this year after three injury-riddled seasons.
Chicago also exercised a $9.5 million option on right-hander Gavin Floyd on Tuesday, declined a $10 million option on right-hander Brett Myers and turned down a $13 million option on third baseman Kevin Youkilis, acquired from Boston in June. Myers gets a $3 million buyout and Youkilis $1 million.
Detroit exercised a $6 million option on shortstop Jhonny Peralta and a $3.5 million on reliever Octavio Dotel and also extended manager Jim Leyland's contract through next season.
Atlanta exercised options on catcher Brian McCann ($12 million), right-hander Tim Hudson ($9 million) and left-hander Paul Maholm ($6.5 million).
Texas declined options on right-handers Scott Feldman ($9.25 million) and Yoshinori Tateyama ($1.2 million).
Oakland allowed left-hander Dallas Braden and right-hander Joey Devine to become free agents. The pair, who missed 2012 because of injuries, refused minor league assignments.
The Los Angeles Dodgers brought back Brandon League, re-signing their closer to a $22.5-million, three-year deal on Tuesday.
League, acquired by the Dodgers from the Seattle Mariners at the July trade deadline, went 2-1 with six saves and a 2.30 ERA in 28 appearances with Los Angeles. He was especially effective over the final 1 1/2 months of the season, posting a 0.55 ERA in 15 appearances in September and October, sixth-lowest in the National League during that stretch.
"He's somebody we really thought we needed to have here and to build a bullpen," Dodgers general manager Ned Colletti said.
League, who was 2-6 with 15 saves and a 3.13 ERA in 74 games with the Dodgers and Seattle this season, will be the designated closer, Colletti said. League has saved 52 games, finished 99, and posted a 2.97 ERA in 139 appearances over the last two seasons.Suggest a correction