Kelly is the son of Don and Bonnie Ward, who have been active in theatre in San Diego for decades. Along with his brother Kirby Ward (For the Boys - Hier, aujourd'hui et pour toujours (1991)) and sister, Kelly appeared in numerous theatre productions in and around San Diego while growing up. They were often either directed or choreographed by his parents. He appeared in productions in San Diego along with the likes of Brian Stokes Mitchell (of Trapper John, M.D. (1979)) and Kathy Najimy (Sister Act (1992), et al) in productions by the San Diego Youth Theatre and the Starlight Civic Opera Association. It was in the Starlight production of "Fiddler on the Roof" (1974) that Kelly met his future wife, Annette Foster. Kelly's breakout role was that of Putsie in Grease (1978), starring alongside John Travolta and Olivia Newton-John.
