Cobb entered films in the 1930s, successfully playing middle-aged and even older characters while he was still a youth. He was cast as the Kralahome in the 1946 non musical film Anna and the King of Siam. He also played the sympathetic Doctor in The Song of Bernadette and appeared as Derek Flint's (James Coburn) supervisor in the James Bond spy spoofs In Like Flint and Our Man Flint. He reprised his role of Willy Loman in the 1966 CBS television adaptation of the famous play Death of a Salesman, which included Gene Wilder, James Farentino, Bernie Kopell, and George Segal. Cobb was nominated for an Emmy Award for the performance. Mildred Dunnock, who had co starred in both the original stage version and the 1951 film version, again repeated her role as Linda, Willy's devoted wife.

Cobb was born in New York City, to a Jewish family of Russian and Romanian extraction. He grew up in the Bronx, New York, on Wilkins Avenue, near Crotona Park. His parents were Benjamin (Benzion) Jacob, a compositor for a foreign-language newspaper, and Kate (Neilecht). Cobb studied at New York University before making his film debut in The Vanishing Shadow (1934). He joined the Manhattan-based Group Theatre in 1935.

Cobb performed summer stock with the Group Theatre in 1936, when they summered at Pine Brook Country Club in Nichols, Connecticut. During World War II, Cobb served in the First Motion Picture Unit of the United States Army Air Forces.

Lee J. Cobb's wife from 1940 to the 1950s was Yiddish theater and film Actress Helen Beverley (1916—2011). They had a daughter together, Julie Cobb.

Cobb was accused of being a Communist in 1951 testimony before the House Un-American Activities Committee (HUAC) of the U.S. House of Representatives of the Congress, by Larry Parks, himself an admitted former Communist Party member. Cobb was called to testify before HUAC, but refused to do so for two years until, with his career threatened by the blacklist, he relented in 1953 and gave testimony in which he named 20 people as former members of the Communist Party USA.

Following the hearing, he resumed his career and worked with Elia Kazan and Budd Schulberg, two other HUAC "friendly witnesses", on the 1954 film On the Waterfront, which is widely seen as an allegory and apologia for testifying.

In August 1955, while filming The Houston Story, Cobb suffered a heart attack and was replaced by Gene Barry.

In 1957, he appeared in Sidney Lumet's 12 Angry Men, the unique trial jury deliberations drama, as the abrasive Juror #3. In 1959, on CBS' DuPont Show of the Month, he starred in the dual roles of Miguel de Cervantes and Don Quixote in the play I, Don Quixote, which years later became the musical Man of La Mancha. Cobb also appeared as the Medicine Bow, Wyoming owner of the Shiloh Ranch, Judge Henry Garth in the first four seasons (1962–1966), of the long-running NBC Western television series The Virginian (1962–1971).

In 1968, his performance as King Lear with Stacy Keach as Edmund, René Auberjonois as the Fool, and Philip Bosco as Kent achieved the longest run (72 performances) for the play in Broadway history.

One of his final film roles was that of Washington, D.C. Metropolitan Police homicide detective Lt. Kinderman in the 1973 horror film The Exorcist about a demonic possession of a teen-age girl (Linda Blair) in Georgetown, D. C.

Cobb died of a heart attack in February 1976 in Woodland Hills, California, and was buried in Mount Sinai Memorial Park Cemetery in Los Angeles. He was survived by his second wife, Mary Hirsch. His death came the day before his Exodus (1960) co star Sal Mineo was murdered.

He was inducted, posthumously, into the American Theatre Hall of Fame in 1981.