The 21-year-old midfielder will fill the void left by the sale of Kevin De Bruyne to Manchester City on Sunday.
The move comes on the same day Wolfsburg completed the signing of defender Dante from Bayern Munich.
“Wolfsburg is a new challenge for me,” said Draxler in a press release from his new club. “I would like to continue playing at the highest level and Wolfsburg are offering me excellent prospects and they have an extremely strong team.
“I’m looking forward to playing in the Champions League with Wolfsburg and I want to be challenging for titles here in years to come.”
Wolfsburg’s director of sport Klaus Allofs was delighted to welcome the World Cup winner to his club.
“Julian was the player we wanted and, due to the sale of Kevin De Bruyne, we have been able to sign him,” he said.
“We’re delighted that he has chosen Wolfsburg and therefore to stay in the Bundesliga and we are convinced that Julian will develop further here.”
Wolfsburg beat off competition from Juventus to sign the Germany international, who has been capped 15 times by his country in addition to playing 170 games in all competitions for the Royal Blues.
“Julian is somebody who can play in practically any position across the front line,” said Wolfsburg coach Dieter Hecking.
“He fits the bill perfectly for the kind of player we were looking for and for our style of play.
“In spite of his young age, he already has a lot of experience.”
Schalke revealed the club were left with little choice after the player had pushed for a move.
General manager Horst Heldt told schalke04.de: “We will not be disclosing information about the transfer fee, but we can say that it is the biggest amount we’ve received for a player at Schalke. Moreover, we have complied with Julian’s desire to move to another club.
“At the end of last season, Julian came to me and explicitly said that he wanted to leave the club. I told him we would consider any offers that came in for him, but I also tried to convince him until the end to stay in light of the new sporting direction that we’re now taking.
“Julian acknowledges the positive developments that we’ve seen in recent months, but this did not change his stance. Instead he repeated his desire to leave.
“It was clear for us that we would only agree to any transfer if the offer matched our valuation. Julian Draxler has been essential in Schalke’s sporting success in recent years, including a DFB-Pokal title and three years in the Champions League.
“We would like to thank him for his services and wish him all the best for his sporting future.”