Magath, who has a contract until 2013, was sacked by Schalke on Wednesday following a mediocre Bundesliga season and despite their Champions League last eight and German Cup final qualification.
"I would not have taken over any other club apart from Wolfsburg," Magath told a large crowd of reporters during his speedily arranged official presentation. "It is difficult to take over at this stage. Time is running out."
"It is now the time to focus on our relegation battle. We have to shoot out of the blocks against VfB Stuttgart," said Magath, donning his club-colour green tie as he used to do during his first stint there.
"I still had it in the cupboard," he joked.
Magath will again hold both posts, making him the most powerful individual in the club's sports department, just as he did when he first coached Wolfsburg from 2007 to their maiden Bundesliga success in 2009.
"Structurally Wolfsburg are the opposite of my previous club. It is better structured and arranged. You can integrate much better," he said.
Wolfsburg have failed to find stability since Magath's departure and sacked Steve McClaren earlier this year with Pierre Littbarski briefly succeeding the Englishman.
