In a statement issued through the League Managers Association, Keegan said he had been left with "no choice" other than to leave because of the way the club was being run.
Keegan, 57, who returned to Newcastle as manager in January, 11 years after his sudden departure from the job in 1997, was in charge for 21 competitive matches, winning just six.
Keegan's future had been under the spotlight since Tuesday when the club issued a statement saying he had not been sacked.