The 22-year-old has signed a five-year contract with the German side.
“I am pleased that everything is now perfect,” Berg told the club’s official website.
“HSV are a top club in the Bundesliga and I want good performances and goals to help ensure that we will be as successful as possible.”
“I am very glad that we have signed Marcus Berg. He is a striker who has a desire to score goals,” HSV trainer Bruno Labbadia explained.
“That’s what he has done in the past three years and impressively proved that at the recent European U-21 Championship.”