The exciting duo, both of whom are already starring for the club's reserve side, have agreed professional terms with the Bavarian giants
Austrian midfielder Schopf, 19, has put pen to paper on a deal that will keep him at the Allianz Arena until June 30, 2016.
As for Green, who is currently top scorer in the fourth-tier Bavarian Regional division with 15 goals in 17 games, he has penned a contract that runs until the following summer.
"Alessandro and Julian are two huge talents who have what it takes to make it in the professional game," Bayern sporting director Matthias Sammer told the club's official website.
"We’re delighted these junior internationals have committed to FC Bayern. In turn, the professional contracts are the reward for their ambition and excellent performances in our second team."
Meanwhile, Green has already turned down a senior call-up into Jurgen Klinsmann's United States squad for the friendlies with Scotland and Austria as he is still entertaining the idea of representing Die Mannschaft at senior level.
"I feel honoured by the invitation," said the 18-year-old striker, who has an American father and German mother.
"But they came too early for me. I have not made my final decision of whether to play for Germany or USA - the subject is still open for me."