The 26-year-old forward, who scored nine goals in 26 top-flight appearances last season, has put pen to paper on a four-year deal at the Imtech Arena.
"Nicolai is a player who has shown a constant improvement in the last few years," commented HSV's CEO Dietmar Beiersdorfer. "That makes him a perfect fit for us, as we are also a club looking to take things step by step. He'll strengthen our options in attack, particularly with his versatility, pace and shooting. He's a kid who keeps his feet on the ground, in spite of the success he's enjoyed in his career so far."
A former member of Eintracht Frankfurt's youth academy, Müller joined Greuther Fürth at the age of 16, before joining Thomas Tuchel's Mainz in the summer of 2011. The Lower Franconia native netted 24 Bundesliga goals over the course of three seasons with die Nullfünfer, helping the club to a place in the third qualifying round of the UEFA Europa League at the end of the 2013/14 season.
'Delighted to be here'
"Of course I'm delighted to be here and that everything's worked out," said Müller ahead of the next chapter in his career. "I wanted to take the next step and move to a big club in such a city. My talks with the club bosses were very good and I just wanted to try something new. I'm 26 now and I want to improve myself here."
Hamburg, the only club to have competed in every one of the Bundesliga's 51 seasons to date, begin their league campaign away at 1. FC Köln on 23 August.