A promising goalgetter at 1. FC Nürnberg, Drmic has seen his career stall since moving to Bayer 04 Leverkusen in 2014 and then to BORUSSIA-PARK last summer.
The striker made 13 Bundesliga appearances for Gladbach this season, but only four of them were starts and he scored just a single top-flight goal for the Foals. He now hopes the move north will get him back on track.
"Obviously I'm happy that things have worked out and that I'm here. I'm extremely motivated and prepared for the task in hand," said the 23-year-old, who has scored 24 goals in 71 Bundesliga career appearances so far.
"It's a new challenge for me. I didn't get going at Leverkusen and things didn't happen as expected at Gladbach. At Hamburg, I'm getting a fair chance. I'm focusing fully on what happens on the pitch. I'm shutting out everything else that goes on around me.
"Of course I'm looking forward to seeing the fans and the super stadium, but firstly, it’s all about playing. I want to play again and hopefully make a difference."
While Drmic will spearhead Hamburg's challenge alongside Pierre-Michel Lasogga, the forward's Switzerland international team-mate, Johan Djourou, will attempt to keep opposing sides out at the opposite end of the pitch as Bruno Labbadia's men aim to plump up the .
"We're close," admitted Drmic of his Nati colleague. "We'd already spoken about HSV and he told me a couple of nice things about the club. We've also talked about perhaps working together, and now it's come good. I'm happy to have players like him around me in Hamburg. That gives me confidence. I can hardly wait to get out onto the pitch with him and help the team."