The 23-year-old has signed a four-year contract with the Scottish side.
Celtic manager Neil Lennon confirmed after their Champions League play-off win against Shakhter Karagandy that a fee had been agreed with Schalke for the striker.
“The carrot of the Champions League might be a bigger draw for a lot of players now,” he said.
“I think it puts us in an excellent position but they will have to play well to get into that team.”
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.