The team announced the moves Friday, making both players free agents. Encarnacion's deal did not include a buyout, while Gonzalez will receive $500,000.
The team also exercised a $3.5 million option on utility man Leury Garcia, reinstated right-hander Michael Kopech from the restricted list and activated righty Jimmy Lambert from the 60-day injured list. The club lost infielder Yolmer Sanchez on waivers to the Baltimore Orioles.
The 37-year-old Encarnacion hit .157 with 10 home runs during the shortened 60-game season. His .377 slugging percentage was the lowest in his 16-year career and his first time below .450 since 2009.
Gonzalez, 35, had a 4.83 ERA in 12 appearances, including four starts. The 13-year veteran struck out 9.7 batters per nine innings, his best rate since 2009.