The 23-year-old has signed a four-year contract with the German side.
Mancienne underwent a medical at Hamburg on Tuesday and joins the club in a deal worth around £3million.
“HSV is a big, well established club with fantastic fans,” Mancienne told the club’s official website.
“It’s a great challenge for me to be playing for this club.”
Hamburg’s sporting director Frank Arnesen said: “I have followed his development for years and I’ve been aware of his great potential.”
