Gnabry left the Gunners last summer in search of first-team football, and found it with Werder Bremen where he shone for the Weserstadion club.
But those performances alerted Bayern to the 21-year-old winger's undoubtable talent and the Munich giants have not delayed in activating a clause in the youngster's contract.
Gnabry's arrival in Bavaria should smooth the path for Douglas Costa's departure.
The Brazilian wideman is being monitored by Juventus, Barcelona and Liverpool this summer and is expected to leave the Allianz Arena.
Source: Independent
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