The highest-charting version of the song was recorded by the Sammy Kaye orchestra in 1946, although a version of the song recorded by Frankie Laine has become better known over the years, being one of Laine's best-known recordings. It has been recorded by many other singers, including a number of doo-wop groups.

The recording by the Sammy Kaye orchestra was released by RCA Victor Records as catalog number 20-2251, with the flip side "Red Silk Stockings and Green Perfume". It first reached the Billboard Best Seller chart on June 13, 1947 and lasted 17 weeks on the chart, peaking at #2.

The recording by Frankie Laine was recorded on August 27, 1946, with Manny Klein's Orchestra, and released by Mercury Records as catalog number 5007, with the flip side "By the River Sainte Marie". It reached the Billboard Best Seller chart on June 27, 1947 and lasted four weeks on the chart, peaking at #4. It was Laine's first chart hit. Despite the higher chart position of the Kaye version, the Laine version is the widely reported million-seller. The Laine version also appeared on Billboard′s Rhythm and Blues survey.

The recording by Hadda Brooks on the smaller Modern Records label, also peaked at #4 on the R&B chart in 1947.

The Hollies' version, recorded in Abbey Road studios 1st March 1965 appeared on the group's 3rd LP. In South Africa it was released as a single, and went no 1 there in 1967.

Eddie Cochran recorded his version of "That's My Desire" in early summer of 1956 at Gold Star Recording Studios. It was first released in the UK in 1962 on the album "Cherished Memories". The first release in the US was on the album Eddie Cochran On The Air in 1987.

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