Gazidis, who joined the Gunners in 2009, is one of four Premier League figures appointed to the PGB, with the eight-man team also comprising of four Football League representatives.
Tottenham director of football administration Darren Eales, Manchester United chief executive David Gill and Premier League chairman Dave Richards have also been placed on the committee, which advises the FA on various issues within the game.
The board is also responsible for administering the FA Cup, the England national team set-up and the FA's relationship with Fifa and Uefa.
In addition to that role, Gazidis will also serve as one of eight Premier League representatives on the FA Council, who play a significant role in player development.
The council recently voted in support of a significant youth development review which will see small-sided games made mandatory for players up to under-12 level, which is due to be phased in by the start of the 2014-15 season.
Gazidis will continue to perform several other roles within Fifa's Dispute Resolution Chamber, the Legal Advisory Panel of the European Club Association and the Premier League Working Group for Elite Player Performance.
"I am delighted to be joining these important footballing bodies," Gazidis told Arsenal's official website.
"The appointments mean Arsenal will be represented in many of the key debates in the game both here in the UK and in Europe."