The A's also announced Friday they agreed to one-year deals with first baseman Daric Barton and infielder Adam Rosales. Oakland designated right-hander Sandy Rosario for assignment and said it will not offer a contract to outfielder Jermaine Mitchell.
Barton batted .204 with one homer and six RBI for the A's last season. Rosales batted .222 with two homers and eight RBI for Oakland last season.
Resop was 1-4 with one save and a 3.91 ERA in 61 relief appearances with Pittsburgh last year.
Thornton went 4-0 with 16 saves and a 4.53 ERA in 48 relief appearances for Class A Stockton last season.