Morris was a church-choir singer from his youth, trained at the Juilliard School of Music, and graduated from Dillard University in 1958. Early in his career, he soloed with the Harry Belafonte singers. He performed in a number of Broadway musicals, including Hallelujah, Baby! and Ain't Supposed to Die a Natural Death. He also appeared as a high school teacher in the film Cooley High. He had a small role as a police sergeant in The Anderson Tapes (1970).
Morris has appeared in numerous television shows and movies since the early 1970s, but is best known as one of the original cast members of NBC's Saturday Night Live. At least twice on SNL he sang classical music: once a Mozart aria when guest-host Walter Matthau designated him as a "musical guest...in place of the usual crap", and once a Schubert lied while the titles on the screen purported to express his colleagues' displeasure at having to accommodate a misguided request by him. Morris appeared in five episodes of The Jeffersons playing a character named Jimmy.
One of Morris's best known characters on SNL was the Dominican baseball player Chico Escuela. Chico spoke only limited and halting English, so the joke centered on him responding to almost any question with his catch phrase: "Baseball... been berra berra good... to me." Another recurring bit, used in the newscast segment "Weekend Update", involved Morris being presented as "President of the New York School for the Hard of Hearing" and assisting the newscaster by shouting the main headlines, in a parody of the then-common practice of providing sign language interpretation in an inset on the screen as an aid to the deaf viewer.
According to the book Saturday Night: A Backstage History of Saturday Night Live, Morris was frequently unhappy during his tenure on SNL from 1975–1980, and expressed the opinion that he was usually typecast in stereotypical roles.
African-American performers who have followed Morris on Saturday Night Live have at times been publicly concerned with not experiencing the same fate Morris did. Eddie Murphy, for example, told TV Guide in the early 1980s that SNL producer Jean Doumanian "had tried to Garrett Morris me... turn me into the little token nigger."
In 1986, Morris began playing a regular occasional character, "Arnold 'Sporty' James," on the NBC cop drama Hunter, starring Fred Dryer and Stepfanie Kramer. Morris continually appeared as "Sporty" on "Hunter" through 1989.
In 1994, he was shot in an apparent robbery attempt but went on to make a full recovery. In a radio interview, he mentioned that the robber who shot him was eventually incarcerated, and in prison some fans of Morris's who happened to be inmates there teamed up and beat up the robber in revenge.
Morris starred on Martin as Martin's first boss Stan. Morris's shooting had caused him to be unable to continue in the role, and he was written out of the show by having the character become a national fugitive. The scene where he is about to undergo plastic surgery was shot on the hospital bed Morris occupied while recuperating from the 1994 assault. He later reprised the role one last time in a guest appearance during the show's third season. In that particular episode, he is seen walking on a cane (due to his shooting) but the incident was comically parodied by saying Stan was in a police chase and had a car crash.
He was a regular and fan favorite on The Jamie Foxx Show. He played hotel owner, and uncle of Jamie Foxx, Junior King for the entire run of the show.
In 1999, Morris appeared as himself in the fifth episode of the fifth season of the TV series, Space Ghost Coast to Coast.
In 2002, Morris made a cameo appearance on an episode of Saturday Night Live hosted by Brittany Murphy.
As of 2006, he continues to perform regularly in films. He also operates and is the host of his own comedy club, The Downtown Comedy Club in downtown Los Angeles.
On February 9, 2007, Los Angeles mayor Antonio Villaraigosa honored Garrett Morris for his work and contributions to the black community. He declared February 9, 2007 Garrett Morris Day and named The Downtown Comedy Club the official club of Los Angeles.
In 2010, Morris appeared in a television commercial for Miller Lite. The national commercial, titled "PopPop," features Morris alongside actors Stacey Dash and Jason Weaver. The commercial takes a light-hearted look at a family relationship with Morris playing the grandfather, PopPop, and Weaver as his grandson.
, Morris has appeared in an ad for Orbit gum in the United States.