The transfer, reported to be worth around €10m (£8.6m) with a sell-on clause retained by Arsenal, brings the 26-year-old back to a club where he spent last season on loan, scoring seven goals and providing six assists in 31 appearances as Hamburg secured promotion back to the Bundesliga after seven years in the second tier.
Vieira never established himself in north London after joining from Porto for around €35m in 2022, a fee that made him one of Arsenal's more expensive squad additions that summer. He made 49 appearances across three seasons at the Emirates Stadium but managed only two goals and five assists, struggling with the physicality of Mikel Arteta's Premier League and losing his place amid growing competition in Arsenal's midfield.
A first loan spell back at boyhood club Porto in 2024-25 yielded 42 appearances and five goals but did not persuade the Portuguese club to make the move permanent, and it was only once he arrived at Hamburg last season that he finally rediscovered the form that first attracted Arsenal's interest.
Hamburg sporting director Kathleen Krüger said the club were delighted to make the deal permanent.
"Fabio is a football artist in the best sense — a player with outstanding technical ability who can enchant spectators with his feel for the ball," she said. "He proved that impressively in last season's Bundesliga campaign."
Vieira himself described the move as a natural continuation of a relationship that began during his loan spell.
"I'm very happy to be back here. I already know the club, the fans and many of my team-mates, so it feels great to be part of it again," he said. "I knew from the start that there might be a chance for me to come back here. I could feel how much HSV wanted me. Now I'm back and I can't wait to get going again."
The north German club have made a difficult start to their return to the top flight, taking just a single point from their opening two matches, and will be hoping their Arsenal recruit can help arrest that slide.
The move is one of several departures from Arsenal this deadline day, with forwards Gabriel Jesus and Gabriel Martinelli both also expected to leave the club on permanent deals — Jesus to Barcelona and Martinelli to Al-Hilal — as Arteta continues to reshape his squad before Tuesday's cut-off.