Hendriks became a full-time reliever for the first time with Toronto last season and went 5-0 with a 2.92 ERA in 58 appearances.
His fastball velocity spiked when he moved to the bullpen, and the 26-year-old right-hander struck out a career-best 9.9 batters per nine innings. Hendriks is under team control through at least 2020.
Chavez has spent the past two seasons as a swingman with the A's and went 7-15 with a 4.18 ERA in 30 games this year, including 26 starts.
The 32-year-old righty made nine appearances with Toronto in 2012 and had an 8.44 ERA before being acquired by Oakland for cash. Chavez is eligible for arbitration this winter and can become a free agent after the 2016 season.
Earlier in the day, the A's signed left-hander Rich Hill to a one-year, $6 million contract.