The versatile defender will link up with the Bavarian club this summer in order to nail down a first-team spot and further his career.
Angha, 19, has spent three years with the Gunners, making his first-team debut in the Capital One Cup tie against Coventry last Septembe.
He came off the bench in the 2-1 Champions League defeat against Olympiacos but has never nailed down a regular place in Arsene Wenger's plans.
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