The moves, announced Friday, enable the sides to avoid arbitration.
Wieters made the AL All-Star team during a 2012 season in which he batted .249 at set career highs with 23 homers, 83 RBIs and 144 games played.
Davis led the Orioles with 33 home runs and 85 RBIs.
Matusz contributed in the bullpen during the 2012 playoffs. In 18 relief appearances during the regular season, the 25-year-old was 1-0 with a 1.35 ERA.
Patton was 1-0 with a 2.43 ERA in 54 games with Baltimore.