Jeter was born in Lawrenceburg, Tennessee on August 26, 1952. His mother, Virginia (née Raines; May 6, 1927), was a housewife. His father, william Claud Jeter (March 10, 1922 – March 1, 2010), was a dentist. Jeter had one brother, william, and four sisters, Virginia, Amanda, Emily, and Larie. Jeter was a student at Memphis State University (now the University of Memphis) when his interests changed from Medicine to acting. He performed in several plays and musicals at the Circuit Theatre and its sister theatre, the Playhouse on the Square, in midtown Memphis. He left Memphis to further pursue his stage career in Baltimore, Maryland.
Jeter's woebegone look, extreme flexibility, and high Energy led Tommy Tune to cast him in the off-Broadway play Cloud 9 in 1981. Much of his work specialized in playing eccentric, pretentious, or wimpy characters, as in The Fisher King, Fear and Loathing in Las Vegas, The Green Mile and Drop Zone. Occasionally, Jeter was able to stray away from these types of roles for more diverse characters like those he portrayed in Jurassic Park III, Air Bud, and Open Range. Perhaps the most enduring role he starred in on the big screen was when he starred in the classic movie The Green Mile and was nominated along with others on the cast for a Screen Actors Guild award.
Jeter was openly gay and met his partner, Sean Blue, in 1995; they were together from 1995 until Jeter's death in 2003.
He was also a favorite with younger audiences in his role as Mr. Noodle's brother, Mr. Noodle on Sesame Street from 2000 to 2003. He appeared in an episode of Touched by an Angel in 1999 as Gus, an insurance salesman who arrives in Las Vegas in the episode "The Man Upstairs". His last two appearances were in the films The Polar Express and Open Range. Both films were in post-production at the time of his death and, when released, contained a dedication to his memory.
On March 30, 2003, Jeter was found dead in his Hollywood home at the age of 50. Although he was HIV positive, he had been in good health for many years. His partner, Sean Blue, stated publicly that Jeter died after suffering an epileptic seizure.
