She was born Ella Geisman in the Bronx, New York City, and brought up in near-poverty. After a childhood accident, she took up both swimming and dancing as therapy, and made her Broadway chorus-line debut in 1938. After her appearance in Best Foot Forward in 1941, she was selected for the 1943 film version, and followed it up with several other musicals, including Thousands Cheer and Good News (1947). She also played straight roles such as the tomboy Jo in Little Women (1949) and Glenn Miller's wife in The Glenn Miller Story (1954).
In 1945, Allyson caused Hollywood studio chiefs some consternation by marrying actor, singer, director Dick Powell, who was thirteen years her senior and had been previously married to Mildred Maund and Joan Blondell. They had two children, Pamela Allyson Powell (adopted) and Richard Powell, Jr., and remained married until his death in 1963, which led to Allyson's effective retirement from the screen. She later married David Ashrow, a dentist turned actor.