Before becoming an actor, Edelman studied to become a veterinarian at Cornell University, but left during his first year. After serving in the US Army as an announcer for Armed Forces Radio, he enrolled in Brooklyn College as a Theater student, but eventually dropped out. He later worked as a hotel manager, and as a taxicab driver. One of his fares was director Mike Nichols, who in 1963 cast Edelman in his breakthrough Broadway role, as the bewildered telephone repairman in Neil Simon's Barefoot in the Park. He reprised his role in the 1967 film version (starring Robert Redford and Jane Fonda), and appeared in the movie versions of Simon's The Odd Couple (1968) and California Suite (1978). He also appeared in an installment of the Japanese movie series Otoko wa Tsurai yo in 1979.
He remains best known for his three decades in television, usually as a co-star or recurring character (Murder, She Wrote, That Girl, Welcome Back, Kotter, St. Elsewhere, Knots Landing, Love, American Style, and Maude, starring Beatrice Arthur), but occasionally in a lead role. He starred in the 1970s children's series Big John, Little John, as well as The Good Guys with Bob Denver (Denver's first series after Gilligan's Island), in 1969. He also appeared with Bill Bixby and Valerie Perrine in Bruce Jay Friedman's Steambath, a controversial PBS dramedy, during 1973.
Edelman was married to soap opera actress Louise Sorel from 1964 to 1970. He was romantically linked with actress Christina Pickles (his co-star on St. Elsewhere), from the mid-1980s until the time of his death.
Edelman succumbed to emphysema in 1996, at the age of 62.
