The defender moves to the German giants on the recommendation of their new football chief Frank Arnesen, who like Mancienne is leaving Chelsea.
The Dane said: "I know Michael from Chelsea and have followed his development for years.
"I am aware of his great potential."
Hamburg finished eighth in the Bundesliga this season, and Mancienne has outlined his ambition to get them back into Europe as soon as possible.
He said: "Hamburg are a big club with a lot of tradition and some fantastic fans.
"It's a big challenge for me to be able to play for this club.
"It would be great if I could play a part in helping Hamburg get back into Europe."