The German side have bolstered their midfield ahead of next season's Champions League campaign, tying down the youngster with a five-year contract that will run through 2017
The 19-year-old had been closely linked with Lucien Favre's side in recent weeks, and on Friday put pen to paper on a five-year contract that will expire in 2017.
"We competed with a number of top European clubs in our efforts to sign Granit Xhaka, and are happy that we managed to get him to Borussia," Gladbach sporting director Max Eberl said.
Hamburg had a bid for the Kosovo-born midfielder rejected in January before Gladbach joined the race to claim his signature. Xhaka, who will wear the number 34 at his new club, was over the moon with his transfer.
"I am delighted that the contract is now signed," he said. "The decision was not very hard. I decided on Borussia from the start because they are a fantastic club."
Xhaka rose to prominence this season as his Basel side finished ahead of Manchester United in their Champions League group. His transfer fee was not disclosed by Monchengladbach, but is estimated to be in the region of €8.5 million.
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