The deal includes award bonuses. Olson, 26, batted .195 with 14 home runs and 42 RBIs playing all 60 games for the AL West champion A's in 2020.
Olson was eligible for arbitration for the first time. He earned $223,519 in prorated pay last season from a $603,500 salary.
Second baseman Tony Kemp to a $1.05 million, one-year deal after being acquired by the A's from the Cubs before last season and committing only one error in 43 games at second. He walked 15 times to notch a career-best .363 on-base percentage, batting .247 with five doubles and four RBIs in 49 total games.
Oakland won the wild-card round against the Chicago White Sox before losing to the rival Astros in the AL Division Series.
The A's tendered contracts to the remaining unsigned players on the 40-man roster. They have six remaining arbitration-eligible players: right-handed starters Chris Bassitt and Frankie Montas, outfielder Mark Canha, third baseman Matt Chapman, left-hander Sean Manaea and righty reliever Lou Trivino. from a $603,500 salary.