The central defender, 24, arrives after Arsene Wenger's near summer-long pursuit, and shortly after Calum Chambers' loan departure to Middlesbrough.
Arsenal earlier on Tuesday 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 told the club's official website
"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."
Source : PA
Source: PA