Although Wolfsburg kept the details of the transfer undisclosed, it is believed the DFB-Cup holders coughed up a fee in the region of £25m to secure the transfer.
The 21-year-old will be a direct replacement for the departed Kevin De Bruyne, who sealed his move to England with Manchester City earlier this week.
Draxler has expressed his delight at joining the Wolves and underlined his desire to play at the highest level and compete for titles at his new club.
“VfL Wolfsburg is a new challenge for me,” said the midfielder to his new club’s official website.
“I want to continue playing football at the very top level. VfL offers exceptional prospects and an extremely strong team.
“I am looking forward to the Champions League with VfL and I want to be playing for titles here in the coming years,” he added.
Wolfsburg coach Dieter Hecking has also been effusive in his praise for the German international, and also talked up his versatility and the experience he will bring into the side.
“Julian is a guy who can basically be used in all attacking positions and will make our game even more varied.
“He fits perfectly into our score of requirement and our style of play. In spite of his age, he also brings a good deal of experience to the team,” said Hecking.
Draxler has made over a hundred Bundesliga appearances in his career and scored 15 goals. He won the DFB-Cup with Schalke in 2011, and was part of the Germany team that won the World Cup last summer.