Hendriks was 5-0 with a 2.92 ERA in 58 relief appearances with Toronto this season, striking out 71 batters in 64 2/3 innings next to just 11 walks while yielding three home runs.
The 26-year-old right-hander ranked fourth among AL relievers in strikeout-to-walk ratio (6.45) and limited opponents to a .240 average, including .207 against right-handed hitters.
It was the first time Hendriks pitched exclusively in relief after going 3-15 with a 5.92 ERA in 39 games, including 34 starts, over his first four seasons in the Majors.
Chavez, 32, spent half of the 2012 season in Toronto before being traded to Oakland, giving the A's great work out of the rotation and in the bullpen.