Gnabry has now recovered from the serious knee injury which forced him to miss all of the 2014-15 campaign, and having not featured for the Gunners since March of last year.
The 20-year-old has made 18 appearances for Arsenal since joining from Stuttgart in 2011 and becomes Tony Pulis' fourth summer signing, following the additions of Rickie Lambert, James McClean and James Chester.
The German under-21 international will now hope to make his debut when the Baggies face Manchester City on Monday.
