Written and first recorded (as “That’s All Right, Mama”) by Arthur “Big Boy” Crudup (1946).
Hit versions by Marty Robbins (C&W #7 1955), Elvis Presley (UK #3 2004).
From the wiki: “The song was written by Arthur ‘Big Boy’ Crudup, and originally recorded by him in Chicago in September 1946. Some of the lyrics are traditional blues verses first recorded by Blind Lemon Jefferson in 1926. It was less successful than some of Crudup’s previous recordings, but was rereleased under the title ‘That’s All Right, Mama’ and issued as RCA’s first Rhythm & Blues record on their new 45 rpm single format, on bright orange vinyl.