First recorded (as a demo) by Otis Blackwell (1957).
Hit version by Elvis Presley (US #1/C&W #1 1957).
From the wiki: “‘(Let Me Be Your) Teddy Bear’ was written by Kal Mann and Bernie Lowe, and first recorded as a demo – at Mann and Lowe’s request – by Otis Blackwell (‘Fever‘, ‘Handy Man‘, ‘All Shook Up‘). Written for Elvis Presley’s second feature film, the semi-biographical Loving You, the song was a #1 hit for Presley during the summer of 1957, staying at #1 for 7 weeks, and was the third of four #1 songs Presley would have that year.
“Otis Blackwell won talent contest at Harlem’s Apollo Theater as a teenager and was encouraged by NYC songwriter Doc Pomus to begin writing. He wrote and sang own songs, played piano, but without much success until Christmas, 1955 when he sold six tunes for total of $150. One of them was Elvis’s #1 smash ‘Don’t Be Cruel’. Blackwell recalls (from Riding on a Blue Note: Jazz and American Pop: ‘It turned out we sounded alike, had the same groove, so I began doing demos for Presley from other publishers … The cat was hot, that’s why his name is on the songs. Why not? That’s the way the business is anyway.’
“Although Blackwell did not compose ‘Teddy Bear’, he was prolific songwriter (who would sometimes use the white-sounding pseudonym ‘John Davenport’), copyrighting more than a thousand compositions in his career: ‘Don’t Be Cruel’, ‘All Shook Up‘, ‘Handy Man‘, ‘Great Balls of Fire’, ‘Fever‘, and more, that became hit recordings for Presley, Jerry Lee Lewis and Jimmy Jones.”
Elvis Presley, “(Let Me Be Your) Teddy Bear” from Loving You (1957):