He served in the United States Marine Corps and later in the Alaska Air National Guard.
Kelly also served as the Senate Rules Committee chair from 1981-1982, 1985-1986, and 1993-1996.
Kelly decided not to seek reelection in 2000, and instead began working as a lobbyist representing medical and insurance clients.
Kelly died at his home, in Anchorage, Alaska, from heart problems.
Kelly married Lisa Nelson and the couple had two children.