The 21-year-old scored 17 goals in 33 league games this season, despite his side's relegation from the Bundesliga.
And, having caught the eye in his debut season in the German top flight, Drmic has now signed a five-year contract with Leverkusen.
"With this commitment, we have set a clear sign of our future direction ," said Leverkusen managing director Michael Schade. "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."
Drmic's signing follows earlier confirmation that Brazilian full-back Wendell would join the club for next season.
