Logan began his directing career as a student at Princeton University. He formed a student theater with the students, Henry Fonda, James Stewart and Margaret Sullavan. After graduation, he went to Moscow to study directing Konstantin Stanislavsky. Back in the U.S., he began to stage plays on Broadway. Especially as a musical director, he enjoyed great success.
His film work was not nearly as numerous as his theater work. Nevertheless, he received an Oscar nomination for his film Picnic (1955 ) and won for the same film Golden Globe Award. In the 1930s, he had worked as a dialogue director in Hollywood, for example, In the Garden of Allah with Marlene Dietrich and Charles Boyer.
Logan was married from 1945 until his death with the actress Nedda Harrigan.