Di Matteo took over the reins in October with the club in eleventh place in the Bundesliga table, and they finished in sixth, qualifying for the Europa League.
In a statement Di Matteo, who had another two years to run on his contract, said: ???In the last two days [general manager] Horst Heldt and I not only discussed the last seven months, but more importantly turned our attention to planning the new season.
???I presented an idea for a possible successful future and the necessary conditions to put that idea into effect. Despite the fact that my discussions with Horst Heldt were constructive, at a certain point it became clear that the club’s view differed and would be unable to create those conditions in the foreseeable future.
???The frustration at the club after an unsatisfactory second half of the season is too great.
???With the club unable to create what I consider to be the necessary conditions it is not possible to guarantee the success expected by a club like Schalke 04. Therefore I think a fresh start is best for a club and its supporters who have become very close to my heart.???
Heldt added: ???Roberto had a clear vision of the club???s future. When it became obvious that we had different views on the future of the club he always had the best interests of the club in mind regarding potential solutions.???
Heldt insisted that reports suggesting he had sacked Di Matteo were wrong.
???All reports about a dismissal or a sacking of Roberto were completely untrue. Only Roberto???s decision to step down led to this situation of Schalke 04 having to look for a new head coach,??? he said.
???Roberto Di Matteo took over in October 2014 with the club in 11th place. The situation was more difficult than outsiders could imagine. We had a lot of serious injuries and other problems.
???Thanks to Roberto???s work we found winning ways again. In the Champions League we qualified for the round of the 16 and in defeating Real Madrid 4-3 at the Bernabeu nearly kicked the holders out of the competition.
???At the start of February we climbed to third in the Bundesliga. But after that we had a bad run that we couldn???t really stop until the end of the season. Schalke 04 finished sixth and will play in the Europa League next season.???
Assistant coach Attilio Lombardo and??goalkeeper coach Massimo Battara will also leave the club.