First recorded by Fats Waller & His Rhythm (US #5 1935).
Other hit versions by The Boswell Sisters (US #3 1936), Billy Williams (US #3 1957), Willie Nelson (C&W #26/CAN #25 1981).
Also recorded by Frank Sinatra (1954 & 1962), Bing Crosby with Bob Scobey’s Frisco Jazz Band (1957), Bill Haley & His Comets (1957).
From the wiki: “‘I’m Gonna Sit Right Down and Write Myself a Letter’ was composed in 1935 by Fred E. Ahlert and Joe Young, and has become a standard of the Great American Songbook. The first recording on the song was by Fats Waller & His Rhythm, in a Victor Records recording session on May 8, 1935. It was covered the following year by The Boswell Sisters, reaching #3 on US popular music charts. (Connee Boswell would record a solo version in 1952.)