Andrews attended college there and also studied business administration in Houston, working briefly as an accountant for Gulf & Western. In 1931, he travelled to Los Angeles, California seeking opportunities as a singer. He worked at various jobs to earn a living, including pumping gas at a filling station in Van Nuys. One of his employers believed in him and paid for his studies in opera and also at the Pasadena Playhouse, a prestigious theater and acting school.
Andrews' two signature roles came as an obsessed detective in Laura (1944) opposite Gene Tierney, and as a soldier returning home from the war in the Oscar-winning 1946 film The Best Years of Our Lives. He gave a finely calibrated performance in Where the Sidewalk Ends (1950), but by the 1950s, alcoholism had derailed Andrews' career, and on a couple of occasions nearly cost him his life on the highway. He was forced into supporting roles and character parts in B-movies, albeit good ones (he once said that he'd made more money in real estate than he'd ever made as an actor). In 1963, he was elected president of the Screen Actors Guild. Between 1969 and 1972, he appeared in a leading role as college president Tom Boswell on the NBC daytime soap opera, Bright Promise. In 1972, after four years of sobriety, he became one of the first celebrities to appear in a public service announcement for AA.
Andrews suffered from alcoholism, which he eventually brought under control. In 1972 he appeared in a television public service advertisement on the subject.
In the last years of his life, Andrews suffered from Alzheimer's disease and in 1992, just a shy of his 84th birthday, he died of congestive heart failure and pneumonia at the age of 83.