The 21-year-old striker, who scored 17 goals in 33 league games this season despite his side's relegation from the Bundesliga, had also been linked with Arsenal.
However, Drmic has decided to move to the BayArena on a five-year contract, much to the dleight of Leverkusen managing director Michael Schade.
"With this commitment, we have set a clear sign of our future direction ," he enthused.
"Josip Drmic has proved his class last year in the Bundesliga - he is one of the outstanding goalscorers in the Bundesliga.
"With him, we want to increase our offensive qualities again significantly as the team prepare for the renewed assault on the Champions League."
The Switzerland international started his professional career with Zurich and left his boyhood club for Nurnberg last summer, where he immediately developed into a key player.