Machala, who held the position since July 2010, will remain a major shareholder in the npower League Two club as well as a director, juggling those responsibilities with his other business interests.
Azeem takes over having spent two years on the board as non-executive director.
His priority will be to lead Aldershot through their continued period of financial restructure, including the attraction of new investment needed to further the strategic aims of the Hampshire club.
An official statement from Aldershot read: "On behalf of all the directors, staff and supporters we take this opportunity to formally thank Kris for his dedication and commitment during his tenure as owner and chairman.
"We formally welcome Shahid to the role of chairman and have every faith that with everyone supporting him he will lead the club through a difficult but improving position."
The news comes a week after Shots manager Dean Holdsworth was sacked and replaced with Andy Scott.