Born in Cleveland, Ohio, to the jazz trumpeter Francis Williams, Morris served in the United States Army during the Korean War. While in college at Iowa on the G.I. Bill, Morris was active in college theater and hosted the late afternoon Jazz radio show, "Tea-Time", on the University of Iowa station, WSUI. He co-produced concerts at the university with a student friend. Morris began his television acting career in the 1960s, making guest appearances on numerous TV shows such as The Twilight Zone, Branded and Ben Casey. In 1966, Morris was cast in his most recognizable role as the team electronics expert Barney Collier in the TV series '. Morris, Peter Lupus, and Bob Johnson were the only actors to remain with Mission Impossible throughout its entire run. After Iowa, Greg's first professional stage role was in The Death of Bessie Smith. One of his earliest television roles was a cameo appearance on The Dick Van Dyke Show in the episode "That's My Boy?", where Rob becomes convinced that they have taken home the wrong baby from the hospital. The revelation of Morris' character as the other child's father prompted a record setting bout of laughter from the studio audience. In the 1963–1964 season, he appeared on ABC's drama about college life, Channing, starring Jason Evers and Henry Jones. After Mission: Impossible was cancelled, Morris appeared in several movies and made guest TV appearances before he was cast in 1978 as Lt. David Nelson of the Las Vegas Metro Police, during the 1978-79 season of the ABC TV detective series Vega$, co starring with Robert Urich as Las Vegas detective Dan Tanna and Phyllis Davis as Bea. After the cancellation of Vega$ in June 1981, Morris recovered from a serious car accident on I-15 near Las Vegas. After his recovery, Morris continued to make guest TV appearances in the next decade, including several episodes in the short-lived 1988–1990 remake of the Mission: Impossible TV series, which starred his son Phil Morris. Phil Morris was cast as Grant Collier, the son of Barney. Morris also appeared in two episodes of the TV series What's Happening!! as Lawrence Nelson and in three episodes of The Jeffersons, in which he reprised his role of an electronics expert in a comparison sequel of the Mission: Impossible series. Morris was also a frequent guest star on Password ‘’ Tattletales ‘’ and Password Plus in the 1960s and 1970s. Shortly before his death in 1996, he went to see the film version of ' that starred Tom Cruise. The reports were that he disliked the movie so much that he left the theater early. According to the Associated Press, he said of the movie: "It's an abomination."
