Cambridge was born Godfrey MacArthur Cambridge in New York City on February 26, 1933, to Alexander and Sarah Cambridge, who were immigrants from British Guiana. His parents, dissatisfied with the New York Public School System, sent him to live with his grandparents in Sydney, Nova Scotia during his primary school years. When he was 13, Cambridge moved back to New York and attended Flushing High School in Flushing, Queens.

In 1949, Cambridge studied Medicine at Hofstra College, which he attended for three years before dropping out to pursue a career in acting.

Cambridge, along with Writer Maya Angelou and actor Hugh Hurd, organized one of the first benefits for Martin Luther King, Jr. held in New York City; according to Angelou, it was held at the Village Gate in the late 1950s and raised $9,000 for King's civil rights movement. (On his 1964 album Ready Or Not, Cambridge joked he was supporting Barry Goldwater, saying that the GOP presidential nominee had "come flat out against slavery...in principle!")

Cambridge appeared on several network television programs, including Car 54 Where Are You? ("The Curse of the Snitkins"), The Dick Van Dyke Show ("The Man From My Uncle"), I Spy ("Court of the Lion"), and Police Story ("Year of the Dragon"). He also had a small speaking part as a member of Sgt. Bilko's platoon in The Phil Silvers Show, 1957 episode "Boys Town". Cambridge gave an acclaimed performance alongside Tom Bosley in the episode "Make Me Laugh" of Rod Serling's Night Gallery, a story about a failed Comedian who looks to a genie for a quick fix to success; the episode was directed by Steven Spielberg. He perhaps reached his largest television audience in a series of comical commercials for Jockey brand underwear.

Godfrey's memorable film roles include The Last Angry Man (1959), in which he played a character called "Nobody Home", The President's Analyst (1967), where he plays a depressed government agent, and Watermelon Man (1970), in which he played the lead character, a white bigot who one day wakes up and discovers his skin color has turned black. He also had a starring role in the 1970 Ossie Davis adaptation of the Chester Himes novel Cotton Comes to Harlem, as well as its 1972 sequel, Come Back, Charleston Blue. Cambridge made a cameo appearance in Director Sidney Lumet's Bye Bye Braverman (1968) as a Yiddish speaking NYC cab driver involved in a car collision with the main protagonists, and another as a gay underworld figure in the 1975 film Friday Foster. His other film appearances included roles in The Busy Body (1967), The Biggest Bundle of Them All (1968), The Biscuit Eater (1972), Beware! The Blob (1972), and Whiffs (1975).

He later appeared in Jean Genet's The Blacks: A Clown Show, giving a performance that earned him an Obie Award in 1961. Four years later he did a stock version of A Funny Thing Happened on the Way to the Forum.

Cambridge married Actress Barbara Ann Teer in 1962; the couple divorced three years later. During the 1970s he remained in semi-retirement, making few public appearances and marrying Audriano Meyers in 1972.

In addition to acting, Cambridge had major success as a stand-up Comedian. By 1965 he was earning "as much as $4,000 a week...in all respects a headliner, working the best places, such as San Francisco's Hungry i and Hollywood's Crescendo." He appeared on The Tonight Show and was introduced by his favorite Actress Joan Crawford on The Hollywood Palace. His routines were imbued with biting sarcasm and the trenchant topical humor that was Common in comedic circles at the time. He was noted for comic lapses from standard educated speech to Black street-speak.

He hosted, financed, and produced Dead is Dead (1970), a drug-awareness film. It gave an uncensored look at the downside of drug abuse, showing actual addicts injecting drugs and going through withdrawal.