Dyke, who held the position of BBC director general between 2000 and 2004, will take over from the departing David Bernstein on July 13.
The 65-year-old former Manchester United director will be required to relinquish his position as a board member with Brentford in order to meet impartiality requirements.
But he has expressed delight at being handed the role and insists he has the relevant experience to succeed with the FA.
“Football has always been a big part of my life whether playing 11-a-side on Sunday mornings or six-a-side on Thursday evenings," he told the FA's official website.
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“I still turn out to play six-a-side some Thursday evenings although at my age I seem to spend more time injured than playing.
“I supported my local team Brentford as a kid where my elder brother was a junior, watched York City while at university and followed Manchester United whenever I could.
“I got involved in how the game was run when I was first involved in buying sports rights as Chairman of ITV Sport in the late eighties and later at the BBC.
"I learnt a lot in the years when I was on the Board of Manchester United and have seen the other side of the professional game at Brentford.”
Current chairman Bernstein, who will step down after two-and-a-half years due to rules forbidding chairmen from staying in the role beyond the age of 70, also hailed Dyke's appointment.
“I would like to congratulate Greg Dyke on his nomination to succeed me in July as FA Chairman. I wish him every success in this stimulating but demanding role," he said.
“I will ensure that the handover is dealt with efficiently to help in maintaining the stability that has been achieved by The FA since 2010.”