The song was published in 1928, and was first performed later that same year by vocalist Ruth Etting. However, the most famous rendition of this song was recorded early in 1929 by singer Helen Kane, who was by that time at the peak of her popularity. Kane’s childlike voice and Bronx dialect eventually became the inspiration for the voice of cartoon character Betty Boop (most famously using Kane’s famous catchphrase Boop Boop a Doop).
From January 9, 1929 to December 21, 1929 Jack Haley and Zelma O’Neal sang “Button Up Your Overcoat” on Broadway in the musical Follow Thru. They reprised the song in the theatrical release which opened on September 27, 1930 which was also one of the first movies in Technicolor.
The composition was arranged and recorded by John Serry, Sr. with his ensemble for Dot Records for a 33 RPM vinyl recording entitled Squeeze Play in 1956.
The Bonzo Dog Doo-Dah Band recorded a popular cover version in 1966 as the B-side of their “Alley Oop” single. (source Wikipedia)