The club has undergone an extensive review of on and off-field operations since the end of a disastrous 2010 season.
Bowers met with the Lions' board on Tuesday with those discussions leading to his departure.
Former Richmond chief executive Steven Wright has been appointed to lead the club in an interim capacity while a new chief executive is sought.
"Michael has been an asset to this club over a long period of time and has overseen some of the most successful years in our club's history," chairman Angus Johnson said on Wednesday.
"The club acknowledges his wonderful service and we wish him well in whatever path he decides to take in the future.
"Now we are presented with an exciting opportunity to employ a new CEO who will lead the club into a new era.
"As a club we have made some major changes in recent times and we are really excited about the future. We are all united behind the vision of returning the club to a successful position on and off the field."
Both Bowers and the board came to the conclusion that it was an appropriate time to inject some new blood into the role.
"The Brisbane Lions have been a huge part of my life over the past decade and I am grateful to have had the opportunity to be part of such a successful organisation," Bowers said.
"While I've been fortunate to enjoy an extended period at the helm, I also recognise that the role of CEO at any football club is one that has a life span.
"It seemed an appropriate time to step aside given the club is going through a period of considerable change following an extensive review process. It will enable a new CEO to take charge of the Lions and hopefully achieve further success both on and off the field.
"On a personal note, I am looking forward to embarking on a new professional challenge."
The club will launch a nationwide search for a new chief executive with Wright, who was at Richmond for five years, not in the running for a permanent role due to business commitments in Queensland.
