Benn will take up his role on 1 May having been a non-executive director since July 2008. At Festival Republic he is responsible for Reading and Leeds festivals as well operational responsibly for Glastonbury.
Benn takes over from David Bernstein, who was appointed FA chairman earlier this year.
The stadium ran over budget and over time when it was built and has been forced to host events to recoup the cost despite complaints from football players, fans and staff.
"Melvin has great experience in staging the best in entertainment events," said Wembley Stadium managing director Roger Maslin.
"I look forward to working with him to further the progress Wembley Stadium has made in being the ultimate venue for the fans, the sports men and women and the artists that grace this fantastic stadium."
The news follows the NFL’s revelation that it will play another regular season game at Wembley this year – the fifth consecutive since the Stadium re-opened in 2007. The Tampa Bay Buccaneers are the designated home team against the Chicago Bears on Sunday 23 October.
As well as staging The FA Cup Final, Champions League Final and England’s crucial Euro qualifier against Switzerland this summer, the Stadium is hosting eight nights of Take That in July.?
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