The 19-year-old, who joins the Foals from Swiss champions Basel this summer, was initially named in the Switzerland squad for London 2012. However, Gladbach have requested he be released to allow him to focus on affairs at his new club ahead of the 2012/13 season.
"They were hard but fair negotiations," said Gladbach's director of sport Max Eberl after successfully discussing Xhaka's release with the Swiss FA.
"We are pleased Granit will be staying here in Monchengladbach. For Borussia, but also for Granit personally, this is a pleasing and important decision."
Xhaka is set to fill the void in the Gladbach side left by the sale of Marco Reus to Bundesliga champions Borussia Dortmund.