The A's have now agreed to terms with all of their arbitration-eligible players after Friday's announcement.
Blevins finished 5-1 with a 2.48 ERA last season. The 29-year-old has a 3.35 ERA in 214 career games, including career-highs in wins, innings pitched (65.1) and strikeouts (54) last season.
Moss joined the A's in June and batted .291 with 21 home runs and 52 RBI in just 84 games. The 29-year-old spent parts of five seasons in the majors with Boston (2007-08), Pittsburgh (2008-10) and Philadelphia (2011) before having his breakthrough season with Oakland last year. He had just 15 home runs and 78 RBIs before the season.