The lyrics were written by Johnny Mercer with music by Rube Bloom.
[4] History of the song according to The Billboard, September 28, 1940 issue, page 34: Four years ago (1936) "Fools Rush In" was known as "Shangraila," composed by Ruby Bloom and introduced in one of the production numbers at the Chez Paree, Chicago.
Little was heard of it until this past summer when Ruby played it for Bregman, Vocco and Conn, New York music publishers, who suggested that new lyrics be written.
Johnny Mercer was called in and he supplied the words, which have been widely accepted by the public.
(The words originate in "An Essay on Criticism", written by Alexander Pope in the 18th century.)