Arsene Wenger says Arsenal have signed a "great player but have prepared well for the future" with the addition of Shkodran Mustafi.
The centre-back, who won the 2014 FIFA World Cup with Germany, joins for an undisclosed fee subject to the completion of regulatory processes.
Mustafi, 24, made 64 league appearances in two seasons with Valencia, and is returning to England after spending time at Everton's academy.
See: Wenger says Mustafi is at right age | How well do you know Mustafi? | Mustafi models Arsenal kit
Mustafi is Arsenal's fifth recruit of the summer transfer window, and second of the day after Lucas Perez signed from Deportivo La Coruna.
"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," Arsene Wenger told arsenal.com of the 27-year-old forward.
Perez scored 17 goals in 36 league appearances last season.
Both signings will hope to feature for their new club after the international break when Arsenal host Southampton on Saturday 10 September.
See: Photo gallery of Perez in Arsenal colours | Exclusive Perez interview