The player, who has been handed the number eight jersey, has signed a five-year contract following the two clubs' agreement of a transfer fee at the end of last month.
Schalke coach Horst Heldt was pleased to have finally secured the player's transfer and believes that he can develop well as a footballer at the club.
"In the form of Leon Goretzka we're delighted that, alongside Max Meyer, another incredible young talent has decided to play his trade with FC Schalke 04," Bundesliga.com quotes Heldt as saying.
"Leon belongs amongst the most talented players in the whole of Germany and has a huge amount of potential. There were several clubs interested in acquiring his services, but believes he has the best opportunity to develop himself further as an athlete with us."
Goretzka has been capped by Germany at every level up to Under-19s.