from Wikipedia:

"Shine On, Harvest Moon" is the name of a popular early-1900s song credited to the married vaudeville team Nora Bayes and Jack Norworth. It was one of a series of moon related Tin Pan Alley songs of the era. The song was debuted by Bayes and Norworth in the Ziegfeld Follies of 1908 to great acclaim. It became a pop standard, and continues to be performed and recorded into the 21st century.