Die Wolfe parted company with the 59-year-old after a poor start to the Bundesliga campaign, which saw them languishing in bottom of the Bundesliga.
Kostner, who was in charge of the reserve team, said that Magath "agrees" with his decision to take over the reins at the Volkswagen Arena.
"I was in the sauna, and about to head to lunch, then watch a match between Hannover II and Bremen II," he told Wolfsburger Allgemeine Zeitung.
"I switched on my mobile and I had Francisco Garcia-Sanz (Wolfsburg board member) asking to call back.
"I did that and they told me Magath was no longer the coach and asked if I wanted to take over. It is my duty to help, and I think, Felix Magath agrees with that."
Wolfburg beat Fortuna Dusseldorf 4-1 away from home this afternoon.