Kostner was installed as the club's caretaker coach following Magath's resignation, which came after a run of four defeats in a row which culminated in the 2009 Bundesliga champions dropping to the foot of the Bundesliga.
It is nothing new to Kostner, who stepped in towards the end of the 2009/10 season after Armin Veh was dismissed, and successfully saved the club from relegation.
Now, he hopes to repeat that and revive the club's fortunes, starting at Fortuna Dusseldorf on Saturday.
"I felt it was my duty to take over and I will try to repay the faith shown in me," he said.
"Words no longer count for anything. We need to turn those into action on the field.
"We need to pull in the same direction and try to get the three points."
Wolfsburg started the season with ambitions of European football next season, but with only one win on the opening day of the season, the decision to part company with Magath was almost inevitable.
Fortuna's only goal this season is to avoid relegation, and they are on course for that with only two defeats in eight games.
Their coach Norbert Meier certainly does not have to fear a similar fate to Magath either after becoming the club's longest-serving coach in history this week.
Meier has been in charge of the club for over five and a half years, but one thing is still missing from his CV - a home win in the Bundesliga.