"I think I have good reasons for my decision," Magath told a news conference on Wednesday.
"From the start, my common goal with the Wolfsburg board was to lead the club to the top of the Bundesliga. No one, including myself, thought this would be possible within two years."
Magath has enjoyed unexpected success with Wolfsburg this term, leading the outsiders to the Bundesliga summit, three points ahead of second-placed champions Bayern Munich with four matches left.
Pre-season favourites Schalke fired coach Fred Rutten and manager Andreas Mueller in March after a disappointing run in domestic and international competitions.
The decision was not a surprise following days of intense speculation as to whether Magath would stay on at Wolfsburg where he had a contract until 2010.
The former Bayern Munich coach, who has built a reputation as one of the most demanding and driven managers in the Bundesliga, will remain at Wolfsburg until the end of June.
The 55-year-old joined the "Wolves" in 2007 and has turned them into a formidable team.
They equalled the Bundesliga record for most consecutive victories in a season after a 10-match winning streak following the winter break to top the standings.
Wolfsburg, who are capable of demolishing any Bundesliga side on their day, have the season's best attacking record, having scored 66 goals so far, and the third best defence.
They also have the league's top two strikers with Brazilian Grafite netting 23 times and Bosnian Edin Dzeko adding 19.
As well as being Wolfsburg head coach, Magath was also the manager and director of football giving him complete control.
