Devine was projected as the team's closer for 2009 but missed the entire season after undergoing reconstructive elbow surgery in April, performed by Dr. James Andrews.
Devine went 6-1 with a 0.59 ERA and one save for the A's in 2008. He struck out 49 with 15 walks in 45 2/3 innings.
He is the first of Oakland's six arbitration-eligible players to agree to terms for 2010. The other five players are right-handed pitchers Santiago Casilla and Michael Wuertz, and outfielders Jack Cust, Rajai Davis and Scott Hairston.