The 20-year-old will play for the Bundesliga side for the next 18 months, during which he has the chance to convince them to make the move a permanent one since Gladbach have also secured themselves an option to buy.
"Alexander Ring is a technically strong, versatile midfielder who made a name for himself last year with his performances for his club and country in Finland," said Gladbach's director of sport Max Eberl.
"We are delighted to have managed to sign him."
The attacking midfielder was born in Finland but grew up in Germany before moving back to his nation of birth in 2009.
He now returns to Germany where he will be aiming to fill the void which will be left by the departure of Germany international Reus who will move to Borussia Dortmund next June.