The 18-year-old banged in 21 goals in 21 games last season for the Cottagers' youth team.
But after attracting interest from elsewhere, the Englishman snubbed a new deal at Craven Cottage in favour of a move.
Biereth will become the latest in a steady line of attacking talent to come through the Gunners academy, with an emphasis having been placed on promising strikers.
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