First recorded by The Jan Garber Orchestra (US #1 1926).
Other popular versions by Ipana Troubadours (US #10 1926), Art Mooney (US #3 1948), Little Richard (US #41/R&B #12/UK #2/NOR #1 1958), Bobby Darin (US #42/UK #40 1962), Wing and a Prayer Fife & Drum Corps (US #14/Soul #32 1976).
From the wiki: “‘Baby Face’ was written by Harry Akst, the lyrics by Benny Davis. The song was published in 1926, and first became popular that same year when recorded by the Jan Garber Orchestra. It has since been covered by many recording artists, including Al Jolson, The Revelers, Bobby Darin, and Wing and a Prayer Fife & Drum Corps. Swan Districts, an Australian Rules club in the WAFL since 1934, bases its club song on this tune.