Track Description Available in: "That's All Right" is the name of the first commercial single released by Elvis Presley, written and originally performed by blues singer Arthur Crudup. Presley's version was recorded on July 5, 1954, and released on July 19, 1954 with "Blue Moon of Kentucky" as the B-side. It is #113 on the 2010 Rolling Stone magazine list of the "500 Greatest Songs of All Time".