The central defender, 24, arrives after Arsene Wenger’s near summer-long pursuit, and shortly after Calum Chambers’ loan departure to Middlesbrough.
Arsenal had earlier secured the signing of Lucas Perez from Deportivo La Coruna, so Germany’s Mustafi becomes their sixth summer recruit after Granit Xhaka, Rob Holding, Takuma Asano — who has already joined Stuttgart on loan — and Kelechi Nwakali.
“He is at the right age,” Wenger said. “He has good experience.
“He is a very focused player who can play with the ball as well. We have taken a great player but have prepared well for the future.”
In the same way recruiting Perez was considered to have strengthened one of Arsenal’s perceived weaknesses, Mustafi arrives following injuries to fellow centre-backs Per Mertesacker and Gabriel.
The Mustafi deal has taken Premier League clubs’ spending during the summer transfer window beyond £1bn (€1.1bn).
As with Perez, the terms of the Germany international’s transfer have not been disclosed.
“I can’t wait to play for this great club,” said Mustafi.
Wenger added of Perez: “He’s not only a goalscorer, he’s a guy who combines well with partners, who can give a final ball and makes good runs
“He’s a late developer in this position because he has always played on the flanks. He’s got a good eye for goal and had an outstanding season last year in a team that didn’t create too many chances.”
Perez said: “It’s a massive step in my career to come to a club with the history and quality that Arsenal have and be able to play in competitions like the Premier League and the Champions League. I’m very proud and happy to be here.”
Werder Bremen say they are close to concluding the signing of another German, Serge Gnabry, from the Gunners, while Arsenal are preparing to allow Jack Wilshere to leave on loan.
The career of Wilshere, 24, has stalled in recent seasons owing to a series of injuries and Arsenal’s considerable strength in depth in central midfield. He was left out of new England manager Sam Allardyce’s first squad selection on Sunday.
After two substitute appearances so far this season it is believed he and the club mutually agreed a temporary move would be beneficial.
Gnabry, meanwhile, has only a year remaining on his contract, and Bremen’s director of sport Frank Baumann said yesterday: “We’ve got an agreement with the player and we’re confident it will go through.
“We have reached a fundamental agreement with Arsenal, but nothing is signed yet.”
Confirmation of the Mustafi deal came just hours after Middlesbrough announced the signing of Chambers on a season-long loan.
The promising defender, 21, becomes the latest addition to Aitor Karanka’s squad having been dropped following Arsenal’s 4-3 defeat by Liverpool in their opening fixture of the season.
Spaniard Karanka built his reputation as a central defender, and he told Boro’s website: “I’m really pleased.
“It’s a position where we’ve been working towards bringing the right player in.
“We haven’t been in a hurry because Calum was the player we were waiting for, and he’s going to help us a lot.”