Elg was born in 1930 in Helsinki, and raised in Turku by her parents, Åke Elg (né Ludwig), a Finnish pianist, and Helena Doroumova (who was of Russian descent). She was signed to a seven-year contract to Metro-Goldwyn-Mayer in the mid-1950s. In 1957, she won the Golden Globe for the Foreign Newcomer Award – Female. She won another Golden Globe in 1958 for Best Motion Picture Actress – Musical/Comedy for her performance in Les Girls, tying with her co-star, the famed and well-established Kay Kendall.

In 1958, she was nominated for a Golden Laurel as Top New Female Personality. In 1959 she starred alongside Kenneth More in The 39 Steps. In 1975, she was nominated for a Tony Award for her performance as Donna Lucia D’Alvadorez in Where’s Charley?. She appeared in the original Broadway production of Nine as Guido Contini’s mother. In 1989, she had the title role as Lea in Chéri, from a Colette novel as adapted by Anita Loos. In 1980, she played Dr. Ingrid Fischer on CBS daytime drama soap opera Guiding Light. From 1980–82, she played Olympia Buchanan, first wife of tycoon Asa Buchanan, on the ABC soap opera One Life to Live. Her character, held prisoner by Asa for months, had a memorable death sequence, falling over a balcony at a costume party.

Her son by her first marriage to Carl Björkenheim, which ended in divorce in 1958, is Finnish-American jazz guitarist Raoul Björkenheim. In 1982, Elg remarried, to Rocco Caporale, an Italian-born educator and professor of sociology. She lives in New York City.