Glasner is currently in charge of Austrian side LASK Linz and will replace Labbadia, who announced his impending departure from Wolfsburg last month.
The 44-year-old will sign a three-year contract, Wolfsburg confirmed in a statement.
"We have been following Oliver Glasner and his impressive work at Linz for a long time," said Wolfsburg sporting director Joerg Schmadtke.
"Our discussions with him confirmed our positive impression that he is the right person to lead the club into the next stage of its development.
"We are getting a coach with incredible expertise and a real team player."
Glasner has worked wonders at Austrian side Linz, whom he took over in the second division in 2015.
He led them to promotion in his first season in charge, and they now sit in second place in the top flight, behind perennial Austrian champions Red Bull Salzburg.
Having also worked as an assistant coach at Salzburg, the Wolfsburg job will be his first outside his native Austria.
His appointment ends Wolfsburg's search for a new coach after 53-year-old Labbadia announced he would not extend his contract earlier this year.
Labbadia saved Wolfsburg from relegation last season, and they are now in the race for Europa League qualification.