Turkey international Sahin, a product of Dortmund's youth system, joined Real in 2011 but after failing to hold down a starting spot was loaned out to Liverpool.
He returned, again on loan, to Dortmund in January 2013 for an 18-month spell with an option for the German club to buy him.
"We informed Real officials on the sidelines of our Champions League game (on Tuesday) that we will make use of this option," club CEO Hans-Joachim Watzke told reporters.
Sahin's loan period officially ends on June 30.
Dortmund lost 3-2 on aggregate against Real Madrid in the competition's quarter-finals on Tuesday.
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