The 29-year-old Austria international, who arrived at the AWD Arena from Middlesbrough in 2010, was allowed to cancel his contract with Mirko Slomka's team
The former Middlesbrough man still had a year to run on his contract with Mirko Slomka's men, but the club agreed to release the Austria centre-back in order to facilitate a move to the Volkswagen Arena.
"We are sad to be losing a player of Emanuel Pogatetz's quality and we must thank him for his performances for the club in the past two seasons, but we completely respect his decision to leave," Hannover sporting director Jorg Schmadtke told the club's official website.
However, Slomka has moved fast to secure the signature of Brazilian defender Felipe on a four-year contract.
"The fact that he has experience of playing in a European competition [the Europa League] was certainly something that influenced our decision," Schmadtke admitted.
"I am confident that he will become a key part of our team in the Bundesliga and in the Europa League next season."
Meanwhile, Wolfsburg boss Felix Magath is just as confident that Pogatetz, who has penned a three-year contract with the club, will prove just as valuable an addition to his own side.
"He is an experienced player who can organise at the back," the 58-year-old coach told his club's official website.
"He is always very committed, never pulls out [of challenges] and is willing to put himself on the line for the good of the team.
"We are very happy to have been able to convince Emanuel of the prospects he has with Wolfsburg."
The 29-year-old Pogatetz arrived at the AWD Arena in 2010 after five seasons with Boro.