As Malcolm Douglas says, it is a very old song. William Chappell in his "Popular Music of the Olden Time", published in 1855-1859 gives the 1588 and 1609 references that Malcolm quotes and also says that:-
"... it is alluded to in Dekker's comedy, Old Fortunatus, where Shadow says: "Only to make other idiots laugh, and wise men cry 'Who's the fool now?' " which is the burden of every verse. It is thought to be a satire upon those who tell wonderful stories."
And there are still a few of such people about today!
"I saw the man in the moon ...!"
Alan