The 18-year-old enjoyed a remarkable goalscoring campaign with the Cottagers' Under-18 side last term, scoring 21 goals in as many appearances in the league and chipping in with 13 assists.
Biereth also turned out in the Premier League 2 on three occasions for the Under-23s but has now made the switch across London to sign a professional contract with Arsenal.
Speaking to the official Arsenal website, Biereth said: "It feels great and I'm really excited to be here. It's a once in a lifetime opportunity and I couldn't really turn it down.
"I think now with the recent track record of youth going into the first team, I thought it was a great project to try and be a part of."
Biereth amassed a total of 25 goals and 15 assists from 37 appearances in Fulham's Under-18 side, and he also netted once in last year's FA Youth Cup.