The decision came after a vote between all 20 Premiership chairmen, who decide on their four representatives on the board.
The news is a real shock, as Dein is seen as one of the most influential men in English football.
Dein recently received major criticism for his part in appointing the new England manager - as he was perceived to push the claims of Brazilian Luiz Felipe Scolari, who pulled out of the running soon after being interviewed.
Gill, who is already vice-chairman of the G14 Group and an FA council member, is well qualified for the role.
"I am looking forward to working with my fellow board members," said Gill.
He will now sit alongside Phil Gartside, Robert Coar, and Premier League chairman Dave Richards on the FA board as they look to protect the interests of The Premiership.
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