Sherrill is a former All-Star who is coming off Tommy John surgery on his left elbow. He appeared in two games with the Seattle Mariners last season before going on the disabled list. The 35-year-old left-hander 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' 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.
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