Kansas City also exercised the $6.5 million club option on shortstop Alcides Escobar for 2017.
Meanwhile, designated hitter Kendrys Morales and right-hander Edinson Volquez declined their mutual options. Kansas City also declined its mutual option on Kris Medlen despite the right-hander exercising it on his end.
Morales, Volquez and Medlen will all become free agents.
Kansas City also activated third baseman Mike Moustakas (knee), left-hander Tim Collins (elbow) and right-hander Mike Minor (shoulder) off the 60-day disabled list.
Davis, 31, pitched just 43 1/3 innings last season due to forearm issues while posting a 1.87 ERA and 27 saves. Escobar batted .261 and played in all 162 games for the second time in three seasons.