Born Francis Phillip Wuppermann in New York City to the wealthy family which distributed Angostura bitters, he attended Cornell University where he was a member of Phi Kappa Psi fraternity. He then followed his older brother Ralph Morgan into show business, first on the Broadway stage and then into movies. His first film was The Suspect in 1916. His career expanded when talkies began, his most stereotypical role being that of a befuddled but good-hearted middle-aged man. He was nominated for the Academy Award for Best Actor in 1934's The Affairs of Cellini, where he played the cuckolded Duke of Florence and the Academy Award for Best Supporting Actor in 1942's Tortilla Flat, where he played a simple Hispanic man.

Morgan's most famous role was in The Wizard of Oz (1939), where he played the carnival huckster "Professor Marvel", the door warden to the Emerald City, the driver of the carriage drawn by "The Horse of a Different Color", the armed guard leading to the wizard's hall, and the Wizard of Oz himself. Like Margaret Hamilton's Wicked Witch of the West, his characters only appear on-screen for a few minutes in total, but they are show-stoppers. He was so popular that MGM gave him a lifetime contract. Other movies of note include The Shop Around the Corner, The Human Comedy, The White Cliffs of Dover and his last movie, Key to the City, which was released after his death, in Beverly Hills, California.

Like most character actors of the studio era Frank Morgan had numerous roles is many motion pictures. One of his last roles was as a key supporting player in The Stratton Story, a true story about a ballplayer (played by James Stewart) who makes a comeback after losing a leg in a hunting accident.

Having died in 1949 (while filming Annie Get Your Gun), Morgan was the one major player from the movie who did not live to see The Wizard of Oz become an American institution. He was buried in Green-Wood Cemetery in Brooklyn.

He has a star on the Hollywood Walk of Fame at 1708 Vine Street.