Hedison decided he wanted to be an actor after he saw Tyrone Power in the film Blood and Sand. He began his acting career with the Sock and Buskin Players at Brown University before moving to New York to study with Sanford Meisner and Martha Graham at the Neighborhood Playhouse and with Lee Strasberg at the Actors Studio.
His work on the New York stage includes the off-Broadway production of A Month in the Country, directed by Michael Redgrave, which starred Uta Hagen, for which role Hedison won a Theater World Award. Hedison toured with Anita Gillette in Neil Simon's Chapter Two and appeared in the West Coast premiere of Forty Deuce. He toured with Elizabeth Ashley in Come into My Parlour, and was in the world premiere run of Bernard Slade's Return Engagements. He appeared at the Cape Playhouse in 1998 in Alone Together with Anita Gillette. He also starred in he New York City premiere of First Love with Lois Nettleton. He returned to the Cape Playhouse to appear in Tale of the Allergist's Wife (2002), and his most recent theatrical appearance was at Monmouth University's Pollak Theatre, in Love Letters with Nancy Dussault.
After his role in A Month in the Country, Hedison signed a film contract with 20th Century-Fox. His first movie with them was the classic war film The Enemy Below, which also starred Robert Mitchum. He followed that up with the 1958 horror classic The Fly. Other films in which he appeared include The Son of Robin Hood, Marines, Let's Go!, The Lost World, The Greatest Story Ever Told; ffolkes and The Naked Face. Hedison was the first actor to play James Bond's ally Felix Leiter in more than one film (Live and Let Die and Licence to Kill). Hedison as Evan Robley in the TV series Wonder Woman
Much of Hedison's acting career has been on television. In 1961, he appeared with Geraldine Brooks (1925–1977) in an episode of ABC's Bus Stop with Marilyn Maxwell, for which Brooks was nominated for an Emmy Award. He was cast as a counter espionage agent who traveled the world as a Hollywood talent agent in the 16-episode series Five Fingers. He followed that up with a starring role as Captain Lee Crane in the ABC television version of Irwin Allen's Voyage to the Bottom of the Sea with Richard Basehart. The show ran for four years. He also had a semi-regular role on ABC's The Colbys.
In 1990, he was the series host for Phenomenal World. He appeared in the television movie A.D. as well as The Saint Family, The Love Boat, Fantasy Island, The Bob Newhart Show, Charlie's Angels, The A-Team, Knight Rider, and Wonder Woman, among many others. He played Spencer Harrison on the American soap opera Another World from 1991 to 1996. He followed that up in 2004 with a role on The Young and the Restless as Arthur Hendricks. His most recent role was in 2005's The Reality Trap. Also appeared in the 2001 movie "Mach 2". In 2010 he fell victim in prankster Kayvan Novak's Facejacker.