Clarke, who was also Leicester City Chairman, will begin his duties on Sept. 2, two days before England start their 2018 World Cup qualifying campaign against Slovakia under new manager Sam Allardyce.
"I'm delighted to be confirmed at the next Chairman of The FA and I'm relishing the challenge," Clarke told the FA website.
"My experience as a Council member for The FA has given me an insight into the excellent work this organisation undertakes at every level of the game."
David Gill, who had been acting as Chairman after Dyke's departure in July, will return to his duties as Vice-Chairman.
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(Reporting by Ian Rodricks in Bengaluru, editing by Ed Osmond)
