Lindstrom will move to the Autostadt on a one-year loan, while the deal will also include a buy option worth €12m.
Wolfsburg sporting director Sebastian Schindzielorz is very pleased with the reinforcement.
"Jesper has experience from the Bundesliga and at international level. With him we get a dynamic and very versatile player who can cover almost all positions in midfield."
"We are delighted that he is already part of the team and will work with the group in the training camp", says Sebastian Schindzielorz to the Bundesliga club's website.
In Wolfsburg, Lindstrom will be teammates with, among others, Jonas Wind, Joakim Maehle and Andreas Skov Olsen. All four have been in included in the squad for the Danish national team in the past year.
However, Lindstrom has not been involved recently under national coach Brian Riemer. In total, he has played 18 international matches. The most recent international match were against Portugal in March.
25-year-old Lindstrom has played for Brøndby earlier in his career, where he made his breakthrough.