Cust's agreement leaves right-hander Justin Duchscherer as Oakland's only player eligible to file for salary arbitration on Thursday.
The 30-year-old Cust batted .231 with a team-leading 33 home runs and 77 RBIs while also drawing 111 walks and striking out 197 times last year, when the A's finished with their worst record (75-86) since going 74-88 in 1998.
Oakland was last in the major leagues with a .242 batting average and last in the AL with 646 runs. The A's already have upgraded their offense with the signings of left fielder Matt Holliday and DH-first baseman Jason Giambi this winter. Cust was one of eight different starters in left last year, so Holliday provides stability in that spot.
Cust, a left-handed hitter, led the AL in walks and strikeouts, and tied for sixth in home runs.