Dutton adds that both contracts include invitations to minor league spring training.
Sherrill signed with the Seattle Mariners last Dec. but only appeared in two games with the club before sustaining a significant elbow injury that required Tommy John surgery.
Sherrill appeared in 51 games for the Atlanta Braves during the 2011 season, posting an ERA of 3.00 over 36 innings. The 35-year-old has late-inning experience, as he saved 51 games for the Baltimore Orioles between the 2008-09 seasons before they traded him to the Los Angeles Dodgers.
Over nine seasons at the major league level Sherrill has maintained an ERA of 3.77 with 8.9 strikeouts and 4.3 walks per nine innings.
Wheeler spent the 2012 season with the Cleveland Indians, allowing 12 runs on 17 hits with seven walks and two strikeouts over 12 1/3 innings pitched. The 35-year-old spent a majority of the year with Cleveland’s Triple-A affiliate, posting an ERA of 2.32 over 36 appearances.
Wheeler has spent 13 years at the major league level, posting an ERA of 3.89 over that span.