Latessa was born in Cleveland, Ohio. His mother was an automotive upholstery maker. He made his Broadway debut in The Education of H*Y*M*A*N K*A*P*L*A*N in 1968. Additional theatre credits include Follies, Rags, The Cherry Orchard, Damn Yankees, A Funny Thing Happened on the Way to the Forum, Awake and Sing!, Cabaret, and Hairspray, for which he won both the Tony and Drama Desk Award for Best Featured Actor in a Musical.
Throughout the years he also has been featured in several Neil Simon plays, including Chapter Two, I Ought to Be in Pictures, Brighton Beach Memoirs, Broadway Bound, Rumors, and Proposals.
Latessa's screen credits include The Substance of Fire, Alfie, and Stigmata. He has appeared in numerous television movies, including Izzy and Moe, The Trial of Bernhard Goetz, and Pudd'nhead Wilson, and primetime series such Get Smart, Mission: Impossible, Ironside, Spenser: For Hire, The Sopranos, Ed, and Law & Order.