Sherrill is a former All-Star who is coming off Tommy John surgery on his left elbow. The 35-year-old is 19-17 with 56 saves and a 3.77 ERA in 442 career appearances for the Mariners, Orioles, Dodgers and Braves.
Wheeler, who turned 35 on Monday, is 25-43 with a 3.98 ERA in 589 career appearances for the Rays, Mets, Astros, Red Sox and Indians.
Both of the pitchers will attempt to win spots in the Royals' stacked bullpen during spring training.
Taveras, who turns 31 later this month, is a career .274 hitter in seven seasons with the Astros, Rockies, Reds and Nationals.