The 45-year-old Eiland, who replaces Bob McClure, spent the past season as a special assistant to Andrew Friedman, Tampa Bay's executive vice president of baseball operations.
"We are delighted to have Dave join our coaching staff," Royals general manager Dayton Moore said. "He is an extremely talented pitching coach and a proven winner who has the ability to relate to the young pitchers who are transitioning to the Majors. He has also shown effectiveness in working with established pitchers. (Manger) Ned (Yost) and our entire baseball operations staff have strong convictions about Dave's ability to make a positive difference with our pitching staff."
The Royals ranked 27th in staff earned run average (4.44) in 2011.