The A's also announced Friday that they agreed to minor league deals with right-hander Edgar Gonzalez and infielder Wes Timmons and will invite them to spring training.
Magnuson made his major league debut with Oakland last season and had no decisions and a 6.14 ERA in nine relief appearances. He was placed on the 15-day disabled list Aug. 18 with right shoulder tendinitis and missed the remainder of the season.
Gonzalez is 14-25 with a 5.90 ERA in 107 career appearances for Arizona, Oakland and Colorado. He pitched mostly in the minors last season.
Timmons batted .341 with eight homers and 62 RBIs at Triple-A and Double-A for Oakland last season.