"We are sending a clear signal with this transfer," club CEO Michael Schade said in a statement on Monday.
"Josip Drmic proved his worth in the past Bundesliga season and he belongs to the best forwards in the league."
The 21-year old Drmic, who scored 17 league goals for a Nuremberg team who suffered relegation, was on several top German and European clubs' wish list after a stunning individual season.
"With him we want to increase our attacking qualities and bolster the team for next season's Champions League," added Schade, who did not reveal any financial details of the deal.
Leverkusen finished fourth in the Bundesliga to book a spot in the Champions League qualifying rounds next season.
Drmic, who is expected to feature in the World Cup finals in Brazil next month, had joined Nuremberg in 2013 from Zurich.
- Sports & Recreation
- Josip Drmic
- Michael Schade