As early as 1927, aged 20, Morrow acted onstage as Irving Morrow in Pennsylvania. He later appeared in such plays as Penal Law and Once in a Lifetime, as well as repertory in Shakespeare's A Midsummer Night's Dream, Twelfth Night, Romeo and Juliet and Macbeth.

After serving in the U.S. Army during World War II, Morrow spent the late 1940s on the stage and in radio, where he won the title role in the Dick Tracy radio series. He appeared in many Broadway productions, notably Three Wishes for Jamie, Billy Budd, the Maurice Evans production of Macbeth and the Katharine Cornell production of Romeo and Juliet.

Morrow turned to film acting relatively late in his career, commencing with the Biblical epic The Robe in 1953. Often parodied as the 'Cro-Magnon Man' for his prominent brow, Morrow spent much of the 1950s appearing in a mix of A-budget films such as Flight to Tangier (1953) and Captain Lightfoot (1955), 'B' Westerns such as The First Texan (1956) ""Wagon Train", and science fiction films as a leader and screen hero.

Morrow carried over much of his acting persona from his radio days to his film acting roles, where his ability to rapidly alter both the tone and volume of his voice for dramatic effect frequently gave sound editors fits. He entered the science fiction/monster movie genre with This Island Earth (1955), followed by The Creature Walks Among Us (1956), Kronos (1957) and The Giant Claw (1957).

He returned to television for most of his later roles, with six appearances on the religion anthology series, Crossroads. In two episodes, he portrayed the Reverend M.R. Watkinson in "In God We Trust" and the Reverend Richard C. Smith in the series finale, "Half Mile Down" (both 1957). Other appearances were on such series as Bonanza, My Friend Flicka, The Deputy, Daniel Boone, and Police Story. He was cast three times in guest-starring roles on Perry Mason once as Franz Lachman in the 1962 episode The Case of the Ancient Romeo.

In 1958-1959, he starred as Bart McClelland, the fictitious supervisor of construction of the Union Pacific Railroad in the syndicated half-hour Western series Union Pacific, based loosely on a film of the same name. In 1960, Morrow played Tob, the older brother of Boaz in the biblical drama, The Story of Ruth. During the early 1960s, Morrow appeared in such films as Harbor Lights (1963), the Italian comedy Il giovane normale (1969), Blood Legacy (1971), and in a bow to his earlier career, a cameo in the 1971 Monster film Octaman for veteran 1950's Monster movie writer/director Harry Essex.

After the 1974 cancellation of the sitcom The New Temperatures Rising, and completion of filming the low-budget film Fugitive Lovers, Morrow largely retired from acting, though he returned for a 1975 appearance in the series Police Story. His last television role was in 1986, with a guest appearance in the second season of The Twilight Zone. One of the roles he is best known for is his appearance as a Geologist (astronaut) in the first The Twilight Zone episode "Elegy" (1960) of the second season.

He died on December 26, 1993 in Canoga Park, Los Angeles County, California. He was survived by his wife of nearly fifty years, the late Actress Anna Karen Morrow, and their daughter, Mrs. Lissa Morrow Christian (born in 1948). His ashes were scattered off the coast of Palos Verdes.