A member of the Rock and Roll Hall of Fame since 2001 (his induction speech was given by longtime fan Keith Richards), Burton has also been recognized by the Rockabilly Hall of Fame and the Musicians Hall of Fame and Museum.
Sebagai anggota Rock and Roll Hall of Fame sejak 2001 (pidato pencantumannya diberikan oleh penggemar jangka panjangnya Keith Richards), Burton juga diakui oleh Rockabilly Hall of Fame dan Musicians Hall of Fame and Museum.