The 67-year-old Bernstein succeeded David Triesman who resigned this year.
The FA has been without a full-time chairman since Triesman left in May after being taped making unfounded allegations about England's World Cup bidding rivals Russia and Spain which were published by a Sunday newspaper.
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"It's a very great honour and privilege to be asked to take over this role, at what has not been the easiest time," Bernstein told Sky Sports News.
Roger Burden, the acting chairman, was a strong candidate for the job before withdrawing from the process after England's failure to win the right to host the 2018 World Cup this month.
"I will be speaking to a lot of people over the next four or five weeks to get a consensus and a list of priorities to deal with, and I will be very open going forwards after that," he said. "There is a lot to do here."
Bernstein would not be drawn on the FA's relationship with FIFA following England's failure to land the 2018 World Cup finals when they secured just two votes from the Executive Committee, one from their own representative Geoff Thompson.
Former Arsenal vice-chairman David Dein, the international president of England's failed World Cup bid, had been widely considered to be the favourite to get the job.
Sports minister Hugh Robertson welcomed Bernstein's appointment.
"David Bernstein has a strong background both in the business and football worlds," Robertson said in a statement.
"The challenge for him will be to build a stronger Football Association and develop our national game at all levels."
