The 25-year-old became a regular at the heart of the HSV defence after moving to the Volksparkstadion on an initial six-month loan deal in January, making 15 Bundesliga starts. He has signed a three-year contract.
“Anyone who saw Papa play for us in the second half of the season knows what an impetus he’s given to the team and that his winning mentality and passion have rubbed off on his teammates,” said HSV sporting director Jens Todt.
“Papa quickly identified with the club and being able to secure his services is a real victory for the club. Despite being just 25, he is a real leader.”
Watch: Kyriakos came back to haunt parent club Leverkusen on Matchday 19
Hamburg represent Kyriakos' fourth Bundesliga club after Schalke, Leverkusen and, fleetingly, RB Leipzig. To date, the former Olympiakos defender has made 107 Bundesliga appearances, scoring seven goals.