Devine, 27, sat out the last two seasons after undergoing Tommy John surgery on his right elbow. He was 6-1 with a 0.59 ERA in 42 relief appearances for Oakland in '08.
The right-hander has a 2.48 ERA in 67 career appearances, having pitched the first three years of his Major League career with Atlanta.
No contract terms were released, but Devine earned $557,500 in '10.
Oakland now has five remaining players eligible for arbitration: pitchers Dallas Braden, Craig Breslow and Brad Ziegler, outfielder Conor Jackson and third baseman Kevin Kouzmanoff.