Bonnell has given up his positions as chairman, CEO and director of parent company Infogrames Entertainment as well as Atari Inc.
Patrick Leleu has been appointed chairman and CEO in his place.
Bonnell founded Infogrames 24 years ago. He leaves as the company continues to implement the recent debt re-structuring plan which has strengthened its financial position.
"It is with understandable emotions, but also reassurance about the future, that I leave Infogrames," said Bonnell.
"Time for business developers has logically come, after the entrepreneurial period. It's now time for Infogrames to conquer and progress."
Patrick Leleu has been a director of Infogrames since January this year. He was previously the CEO of Bouygues Telecom between 1994 and 2001 and then chairman and CEO of cable network operator Noos between 2001 and 2005.
"I am convinced that Infogrames holds the assets, talents and teams to be competitive in this business and enjoy growth."