The exciting young players, both of whom have already been starring for the German giants' reserve teams, have agreed professional terms with Pep Guardiola's side
Austrian midfielder Schopf, 19, has put pen to paper on a deal that will keep him at the Allianz Arena until June 30, 2016.
Green, who is currently top scorer in the fourth-tier Bavarian Regional division with 15 goals in 17 games, has agreed 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 Bayern. In turn, the professional contracts are the reward for their ambition and excellent performances in our second team."
Green has already turned down a senior call-up into Jurgen Klinsmann's USA squad for friendlies against Scotland and Austria as he is still entertaining the idea of representing Germany at senior level.
"I feel honoured by the invitation," the 18-year-old striker, who has an American father and German mother, told reporters, "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."