March was born Ernest Frederick McIntyre Bickel in Racine, Wisconsin, the son of Cora Brown Marcher and John F. Bickel. He attended the Winslow Elementary School (established in 1855), Racine High School, and the University of Wisconsin-Madison where he was a member of Alpha Delta Phi. He began a career as a banker, but an emergency appendectomy caused him to reevaluate his life, and in 1920 he began working as an extra in movies made in New York City, using a shortened form of his mother's maiden name, Marcher. He appeared on Broadway in 1926, and by the end of the decade signed a film contract with Paramount Pictures.
March was one of the few actors to resist signing long-term contracts with the studios, and was able to freelance and pick and choose his roles, in the process also avoiding typecasting. By this time, he was working on Broadway as often as in Hollywood, and his screen career was not as prolific as it had been.
When March underwent surgery for prostate cancer in 1972, it seemed his career was over, yet he managed to give one last great performance in The Iceman Cometh (1973), as the complicated Irish bartender, Harry Hope. Coincidentally, co-star Robert Ryan was entering the final stages of lung cancer, so the film was the last for both March and Ryan.
Although March died in Los Angeles, California at the age of 77 from cancer, he considered the rural Litchfield County town of New Milford, Connecticut his primary residence since the 1930s. This property was subsequently home to American playwright Lillian Hellman as well as former Secretary of State Henry Kissinger. March was married to actress Florence Eldridge from 1927 until his death, and they had two adopted children.