The Premier League side said the deal has yet to be officially ratified, but terms have been agreed with the 23-year-old.
“Arsenal have reached an agreement with Granit Xhaka to join the club on a long-term contract for an undisclosed fee,” said a statement from the North Londoners.
Xhaka, the son of Kosovo Albanian immigrants, has represented Switzerland 41 times and helped Gladbach to a fourth place finish this season, bringing with it Champions League football.
Gladbach had said last week that they had received an offer for Xhaka, who then admitted he could see himself playing in an Arsenal shirt.
“Granit Xhaka is an exciting young player, already with good Champions League and Bundesliga experience,” said Arsenal manager Arsene Wenger of his first close season signing.
“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.”
The transfer is still to be officially completed but Arsenal have confirmed Xhaka's contract will begin on July 1.
The news comes as the Premier League revealed on Wednesday that Arsenal became the first club to top £100 million ($147m, 132m euros) in earnings from a single season.
Arsenal finished second behind Leicester City meaning they earned less than the champions in merit payments based on their league finish.
But bitter north London rivals Tottenham Hotspur's late-season collapse allowed them to pinch second place and an extra £1.2 million that took their season earnings over the £100 million mark.
The Gunners benefitted from the greatest amount of facility fees, meaning they featured in more live television matches than anyone else with 27 compared to Manchester United's 26, 25 for Manchester City, just 21 for Spurs and a meagre 15 for Leicester.
Manchester City narrowly edged out United for second place in the earnings table with a shade under £97 million, while Leicester were only fifth with a little over £93 million. – AFP
Original source: Arsenal sign Swiss midfielder Xhaka