From Big Bill Broonzy (1893-1958). Composed by Billy Hill and first recorded by the Benny Goodman Orchestra in 1936, the Broonzy version was done sometime in the 1940s or 50s.
Broonzy was a blues and folk singer, born in Arkansas or Mississippi. Moving to Chicago in 1920 he took up the guitar and soon gained a following though his career was limited by the racial barriers of the time. The folk music revival of the 1950s led to a career resurgence and he toured England, where many British musicians who became famous in the 60s, including John Lennon, cited him as an inspiration. With The Glory of Love, Big Bill took an insipid song and made it a joy to listen to.
It's also the version of the song the Coen Brothers chose to have playing over the credits of their 2003 film, Intolerable Cruelty, starring George Clooney and Catherine Zeta-Jones at her most lovely. THC recommends it.