The Turkey international enjoyed a fine season in 2013-14, scoring 11 goals as Hamburg narrowly avoided relegation from the Bundesliga.
Calhanoglu has made no secret of his desire to leave the Imtech Arena, though, openly stating his preference to join Leverkusen.
And the 20-year-old's wish has now been fulfilled, following the likes of Josip Drmic and Vladlen Yurchenko to the BayArena as they aim to impress domestically and in the UEFA Champions League under new coach Roger Schmidt.
"I had a great time at Hamburg but I can take the next step forward at Leverkusen," Calhanoglu told Leverkusen's official website.
"Bayer are a great team who have regularly been in European competitions over the years. Playing for Leverkusen in the Champions League and being at the top end of the Bundesliga represents a big challenge for me.
"I'm really looking forward to it and I'll give my all to help the team."
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