Although born in Burundi, Berahino has represented England up to under-21 level, though is yet to play for the national team at full international level.
FIFA do not allow players to change national teams once they have played a competitive international game.
Berahino, 25, will now be able to take part in Burundi's qualifiers for the 2019 African Cup of Nations, which continue on the 7th September away to Gabon.
The forward had a controversial time in the Premier League, being involved in a lengthy transfer saga with Tottenham Hotspur which threatened the player's relationship with the board at former side West Bromwich Albion.