The 29-year-old Chavez split this season between Toronto and Triple-A Las Vegas. He was 1-1 with an 8.44 ERA in two starts and seven relief appearances for the Blue Jays.
Chavez is 7-11 with a 5.74 ERA in 152 games for Pittsburgh, Atlanta, Kansas City and Toronto.
The deal was announced before the Athletics played at Tampa Bay.
Ross was recalled Thursday to start against Tampa Bay after Bartolo Colon was suspended 50 games on Wednesday for testing positive for testosterone. Ross will work out of the bullpen at Sacramento.
Miller went 2-1 with a 2.16 ERA over 24 games in two earlier stints with the Athletics this season.