The deal is reportedly worth 7.7 million pounds, with Arsenal accepting a significant loss on the 34 million they paid Porto when signing Vieira in June 2022.
Vieira returns to Hamburg after an impressive loan spell last season, during which he scored seven goals and registered six assists in 31 competitive appearances. The 26-year-old finished as HSV's top scorer and joint-leading assist provider as the newly promoted side secured a comfortable 13th-place finish in the Bundesliga.
Despite arriving at the Gunners with high expectations, Vieira struggled to establish himself in the Premier League. He made 49 appearances in all competitions for the Premier League champions but started just five league matches, while he also spent the 2024/25 season on loan at Porto.
Now, following his successful spell in Germany, Vieira has made his return to Hamburg permanent.
"I'm very happy to be back," Vieira said. "I already know the club, the fans, and many of my teammates. It feels great to be a part of it again. I knew from the beginning that there was a possibility for me to come back here. I felt that HSV had made a real effort to bring me back. Now I'm back and can't wait to get started again."
Hamburg sporting director Claus Costa described Vieira as an "absolute game-changer" and said the club were delighted to secure his long-term commitment.
"We all know what we have in Fabio," Costa said. "He was an absolute game-changer for us last season and possesses qualities that add a special dimension to our play."
Meanwhile, Arsenal have wished Vieira well ahead of the next chapter in his career.
"Fabio Vieira has joined Hamburger SV on a permanent deal," read a statement from Arsenal's X account.
"We wish you all the best, Fabio!"
