Obasi, 25, has done well in his loan spell at Schalke, which started in January.
The Nigeria forward is on a temporary deal until the summer but Schalke have the option to sign him on a three-year contract in June.
"He is developing well with us," said Schalke's director of sport Horst Heldt. "Therefore, we have decided to take the option we have to buy him.
"Chinedu is a very important player for us in the attacking midfield, whether it be on the left or on the right.
"We are planning for next season with Chinedu."
The player himself expressed his pleasure at the move.
"I am looking forward to the future with Schalke," he told Sport Bild magazine.
"They are a really big club and a great team who will always be challenging for silverware."