Chiefs Chairman, Dallas Fisher thanked Flexman for his contribution to the club's success on and off the field.
"A role like this is 7-days a week during the season. The board and shareholders thank Andrew for his commitment to the club and wishes to acknowledge the role he has played in the many achievements of the club," Fisher said in a statement.
"I have no doubt he will make a success of his next career move. We also thank his family for their support to him in the role over the past four years."
Flexman said he is proud of what the club has achieved and says it is well positioned for the future.
"I have loved my time with the Chiefs, but it now feels like the right time to hand over the reins.
"I would like to thank the Board, staff, players, sponsors and stakeholders for making my time at the Club rewarding and enjoyable."
Flexman said he'll finish at the club on Friday, 8 September 2017 and is looking forward to a break post season to pursue new opportunities.
Dallas Fisher said The Chiefs will begin the process to recruit the club's next CEO.