The most successful and best-known version of the song was recorded by Tommy Dorsey and His Orchestra, with vocals provided by Frank Sinatra and The Pied Pipers. This recording was released as a Victor 78, 26628A, in 1940. This version stayed at number one for 12 weeks on Billboard, from July 27 to October 12, 1940, and was inducted into the Grammy Hall of Fame in 1982. The song was also released by Tommy Dorsey on V-Disc, V-Disc 582A, with Frank Sinatra and The Pied Pipers on vocals, in February, 1946.Glenn Miller and His Orchestra also recorded a version of the song in 1940 on RCA Bluebird.
The Platters brought the song back to the top 40 in 1961. Al Hirt released a version in (1962) on his Trumpet and Strings. In 1965, Sinatra re-recorded the song for the double album A Man and His Music, complete with faithful reproduction of the celeste and choral accompaniment which characterized the 1940 recording. He also included it on his 1959 No One Cares album. It has been recorded by many other artists since, becoming a standard. Italian-American crossover artist Sergio Franchi covered this song on his 1967 RCA Victor album, From Sergio - With Love.