Poston served as an Air Force pilot in World War II and enrolled in the American Academy of Dramatic Arts after the war. He performed on Broadway in more than a dozen shows, including Will Success Spoil Rock Hunter (1952), the musical Shinbone Alley (1957), Mary, Mary (1962), and Forty Carats (1968).
His last appearance on the Great White Way was in the 1972 revival of A Funny Thing Happened on the Way to the Forum, in which he replaced Phil Silvers in the leading role of Pseudolus. Poston also worked frequently in regional theater and on national tours.
Poston was best known for his television work. He was a member of the cast of The Steve Allen Show, winning an Emmy in 1959 for his work. He co-starred with his friend Bob Newhart on Newhart as handyman George Utley, receiving three Emmy nominations for Outstanding Supporting Actor in a Comedy Series.
His many other television credits included To Tell the Truth, Mork & Mindy, Grace Under Fire, and Coach, for which he received an Emmy nomination for Outstanding Guest Actor. He also appeared in such films as The Princess Diaries II and Cold Turkey.
Poston is survived by his third wife, actress Suzanne Pleshette, and his two children from prior marriages, Francesca and Jason.