Schalke director of sport Horst Heldt has wished Holtby the best of luck at Spurs.
"We have found the best solution for all involved," he said on his club's website.
"Lewis had hinted to us that he would not be against moving immediately, and Schalke have received a decent sum for a player whose contract was due to expire in five months.
"We wish Lewis all the best for the future."
"He always behaved correctly and gave it all he had got for Schalke until the very last day," added Heldt.