The match will go out on BBC1 on June 6 with Gary Lineker as presenter.
The BBC has already signed up the live TV rights to the following England World Cup qualifier, against Germany on September 1.
The corporation will also have live coverage of all England's home internationals from next season, following the deal signed last summer with the FA.
Channel 5 will carry live coverage of England's next World Cup qualifier, which is against Albania later this month.
The BBC is understood to have paid around #3m ($4.3m) for exclusive live TV and radio rights to England's World Cup soccer qualifier against Greece in June.
