The Austria international makes the short trip across Lower Saxony after putting pen to paper on a three-year contract with the Wolves on Wednesday.
"Emanuel Pogatetz is a robust player and a no-nonsense tackler," said Wolfsburg boss Felix Magath.
"He has a lot of experience, especially in Europe, and he will strengthen our defence.
"I am pleased to welcome him into our squad for next season."
Pogatetz played 29 times for the Reds in the Bundesliga last season, totalling 57 appearances since arriving from Middlesbrough in 2010.
And Hannover have not wasted any time finding a replacement for him after they completed the signing of Brazilian defender Felipe Trevizan Martins from Standard Liege for an undisclosed fee.
The 25-year-old played against Hannover in the Europa League last season and left a lasting impression.
"A player with European experience was the priority in our search for a new central defender and I am confident that Felipe will become a leading figure in our side, both in the Bundesliga and in the Europa League," said Hannover director of sport Jorg Schmadtke.
"While we regret that Emanuel Pogatetz has left us, we thank him for his performances for Hannover over the past two years and we respect his choice of changing clubs."
Felipe cannot wait to make his Bundesliga debut for the Reds, who will learn their opening opponents when the fixtures are announced next Tuesday.
"A dream has come true," he said. "I have always dreamt about playing in the Bundesliga and I am delighted now to be part of a big club like Hannover.
"I now hope to be successful with my new club."