Farrell was born in Willimantic, Connecticut, but she moved at an early age to Woonsocket, Rhode Island, which she always publicly and affectionately called her home town. She was elected to Woonsocket's Hall of Fame.
Her parents were vaudeville singers.
In 1942 she made her concert debut on CBS radio where she soon presented her own radio program. During 1947–1948, she toured the US as a concert singer, and in 1949 she toured South America.
Farrell's song recital in New York in October 1950 was enthusiastically acclaimed and secured for her immediate recognition. That year, she also appeared in a concert performance of Berg's Wozzeck as Marie. In 1952, she was engaged by Toscanini for his first and only studio recording of Beethoven's Ninth Symphony with the NBC Symphony Orchestra.
In the 1955 film Interrupted Melody, which starred Eleanor Parker as Australian soprano Marjorie Lawrence, Ms. Farrell supplied the singing voice for Ms. Parker.
As early as 1956 Ms. Farrell appeared before an audience of over 13,000 under the direction of the conductor Alfredo Antonini in a performance of arias fron Giuseppe Verdi's Ernani at the landmark Lewisohn Stadium in New York City .
In 1956 she made her stage debut as Santuzza in Mascagni's Cavalleria Rusticana with the San Carlo Opera in Tampa, Florida. In 1957 she debuted with the Lyric Opera of Chicago; in 1958, with the San Francisco Opera. She made her Metropolitan Opera debut on December 6 1960, singing the title role in Gluck's Alceste. She opened the 1962–63 Met season as Maddalena in Giordano's Andrea Chénier, opposite Franco Corelli. She remained on the Met roster through the 1963–64 season, singing forty-four performance in six roles, then returned in March 1966 for two final performances as Maddalena. Her other roles at the Met included the title role in Ponchielli's La Gioconda, Leonora in Verdi's La Forza del Destino, Isabella in de Falla's Atlàntida, and Santuzza.
Farrell was equally at home singing pop material and was one of the few opera singers who could sing "Old Devil Moon" and other classics and not sound like an opera singer singing pop tunes. She made four Columbia albums in that vein, I'VE GOT A RIGHT TO SING THE BLUES, HERE I GO AGAIN, THIS FLING CALLED LOVE and TOGETHER WITH LOVE.
Throughout the 1960s she was a frequent soloist with the New York Philharmonic under the direction of Leonard Bernstein; she was also a favourite of Thomas Schippers.
With Eugene Ormandy, the Philadelphia Orchestra, and the Mormon Tabernacle Choir, she was a featured soloist in an abridged recording of Handel's Messiah. The other featured soloists were Martha Lipton, Davis Cunningham, and William Warfield.
From 1971 to 1980, Farrell was professor of music at the Indiana University School of Music in Bloomington. From 1983 to 1985, she was professor of music at the University of Maine in Orono. She also made several recordings of blues music late in her career, as well as the duet which was well received with Frank Sinatra on his "Trilogy" album, in which they sang a version of the country music hit "For the Good Times" which introduced her to a new group of fans, especially Sinatra expert Charles Fasciano, who considered this song his personal favorite. She published a memoir, Can't Help Singing, in 1999.
Beginning in 1987 she began to record pop albums again. Her first was for the Audiophile label called WITH MUCH LOVE. She later recorded several albums for the Reference label and they were well-received.
Farrell was married to a New York City police officer.