British media reported Xhaka's transfer fee at about 30 million pounds, which would make the midfield enforcer Arsenal's third most expensive signing behind Mesut Ozil and Alexis Sanchez.
The 23-year-old Xhaka, who has 41 caps, played 36 times for the Bundesliga club, scoring three goals, and captained them to fourth place last season.
"I'm very proud to be joining Arsenal. I cannot wait to move to London, represent this special club and play in the Premier League. I will give everything to help Arsenal win trophies and make the fans happy," he told the club website (www.arsenal.com).
Xhaka is known for an aggressive style of play which has landed him in trouble, with three red cards last season, but Arsenal manager Arsene Wenger felt his experience was vital.
"Granit Xhaka is an exciting young player, already with good Champions League and Bundesliga experience," Wenger said.
"We have been watching him for a long time now and he is a player who will add quality to our squad."
Xhaka bolsters Wenger's options in defensive midfield alongside Francis Coquelin and Mohamed Elneny.
The Swiss international is preparing for Euro 2016 in France next month, having been named in a provisional 28-man squad.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Ken Ferris)
