The 27-year-old is reported to have signed through to 2029, giving Hamburg a proven Ligue 1 goalscorer on a long-term deal despite his recent struggles for form.
Hamburg will pay Nice a fixed fee of €2million, with a further €500,000 available in add-ons — a fraction of the more than €22million Nice paid Lorient for him three years ago.
Moffi's stock has fallen sharply since that move. After scoring 20 goals in his first two seasons on the Côte d'Azur, a ruptured cruciate ligament in the summer of 2024 derailed his progress, and a loan to FC Porto in the second half of last season failed to spark a revival, with the Nigeria international managing just two goals in 13 appearances before the Portuguese club opted against triggering their purchase option.
Hamburg's director of professional football, Claus Costa, explained the thinking behind the move.
"Terem is a striker who is difficult to control because of his physicality, his determination and the way he plays," Costa said.
"He can attack the space in behind, has an enormous presence in the box and brings the necessary quality with his back to goal.
"We are convinced that Terem will give our play extra penetrative power and add further variability to our squad. Now it's about integrating him quickly so we can start the new Bundesliga season as a team with plenty of energy and conviction."
Meanwhile, Moffi stated: "Even though HSV has played a few years in the 2nd division, the club is still a big name, and that everywhere in the world.
"When I told my father about the interest, he immediately knew which club it was about, and he was full of anticipation. For me, that was crazy in a positive way. That's why I'm all the happier now to be a part of the history and the club myself."
The move follows Hamburg's earlier free-transfer capture of Patson Daka from Leicester City, another forward whose stock has fallen considerably since his own big-money switch to the Premier League — the Zambia international once cost Leicester around €30million from Red Bull Salzburg.
Combined, the pair represent a striking partnership assembled largely on reduced valuations, with a peak combined worth in excess of €52million now secured for a fraction of that outlay.
The Nigerian international, who has won 23 caps and scored six goals for his country, joined Nice from Lorient in 2023 after scoring 34 times in 87 appearances for the Brittany club.
He will wear the number nine shirt previously occupied by Robert Glatzel, who has since moved on to Wolfsburg, as head coach Merlin Polzin looks to bring fresh firepower to a Hamburg attack that scored the third-fewest goals in the Bundesliga last season.