The north London side finally put pen to paper on a deal with the Gunners after days of speculation linking him with a transfer to Emirates Stadium.
Xhaka has made 41 international appearances for Switzerland and joined Monchengladbach in 2012 from his hometown club FC Basel.
Arsenal have moved quickly to wrap up their first signing of the summer, and Wenger explained the reasons behind his choice to sign the midfielder and revealed that the Gunners have been tracking him for some time.
Speaking to Arsenal’s website, Wenger said: “Granit Xhaka is an exciting young player, already with good Champions League and Bundesliga experience.
“We have been watching him for a long time now and he is a player who will add quality to our squad.
“We wish Granit a good Euro 2016 with Switzerland and look forward to welcoming him to Arsenal ahead of next season.”
Xhaka captained Borussia Monchengladbach to fourth place in the Bundesliga last season and Champions League qualification in the past two campaigns.
Arsenal ended up second in the Premier League table last season as they pipped Tottenham Hotspur on the final day of the campaign.
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