She was born as Georgina Allan in Glasgow in 1910 (although she later shaved three years off her age.), where she was raised. She began performing under the name Ella Allan as a child.
She went on to become a band singer in music halls. Aged 20, she made her debut in 1930 in the West End of London in Darling! I Love You. She toured Europe in the early 1930s. Logan eventually emigrated to the U.S. and began to sing at various clubs and to record jazz on the British Columbia label (part of EMI).
She then appeared in several Hollywood films, including Flying Hostess (1936), 52nd Street (1937) and The Goldwyn Follies (1938). She appeared in several Broadway shows in the 1930s and early 1940s, but traveled to Europe and then Africa during World War II to entertain the troops. She also appeared on The Ed Wynn Show and The Colgate Comedy Hour in the 1940s and 1950s.
Logan returned to Broadway in 1947 starring as Sharon McLonergan in the original production of Finian's Rainbow, singing the show's most famous song, "How Are Things in Glocca Morra?", among others. The production ran for 725 performances. She did not return to Broadway after that. In 1954, she was cast in a proposed animated film adaptation of Finian's Rainbow and re-recorded the score with Frank Sinatra. But the film was canceled, and the recordings were not released until the 2002 box set Sinatra in Hollywood 1940-1964.
The original cast album was released in 1948, and was Capitol Records' first Original Cast album. She recorded the show's songs for a second time in 1954 for the LP Ella Logan Sings Favorites from Finian's Rainbow, accompanied by pianist George Greeley. It was released by Capitol Records in 1955, (H-561 in the US, and L-561 in Australia). This was the second of her two solo albums.
In the 1950s, she became an international nightclub performer, appearing at such venues as the Copacabana and the Waldorf-Astoria in New York as well as in London and Paris. She appeared on television in May 1956, in London with Louis Armstrong and His All-Stars. In 1965 she was part of the cast of the infamous Broadway flop, Kelly, until her role was cut during out of town tryouts. She continued to work occasionally in clubs, on television, and in theatrical stock productions, into the 1960s.
Her first husband was Charles John Lepsch. She married, secondly, to Fred Finklehoffe, a playwright and producer, from 1942 until the marriage dissolved in either 1954 or 1956. She had no children by either marriage. Her niece is the actress/chanteuse Annie Ross and her nephew was Jimmy Logan, a Scottish actor.
Ella Logan died of cancer in Burlingame, California, aged 59.