The 19-year-old decided to swap Munich for Leverkusen after being told by new Bayern coach Pep Guardiola that he did not feature in his first-team plans.
Can has signed a four-year deal at the BayArena, with the Germany under-21 international declaring that he is relishing the chance to fight for a starting role at his new club.
He told the club's official website: "Bayer Leverkusen are one of the top teams in the Bundesliga and play in the Champions League as well.
"I want to play my part in helping the team to success in each competition they compete in in the years to come."
Bayern have included a clause in Can's contract that would allow them to re-sign the midfielder for a set fee in the future, with chairman Karl-Heinz Rummenigge insisting that they have safeguarded the starlet's future by allowing him to leave.
He said: "Emre Can is one of the biggest talents in German football. We've taken this step to ensure he gains sufficient match practice, as we've done in the past with the likes of Toni Kroos at Leverkusen, Philipp Lahm with Stuttgart and David Alaba at Hoffenheim."
Can made four first-team appearances during his time at the Allianz Arena, including a maiden Bundesliga appearance against Nuremburg in April.