Terry and Kim Pegula -- the owners of Pegula Sports and Entertainment, which operates both teams -- accepted the resignation. The Buffalo News reported that the move came after the company conducted an internal investigation into Brandon's workplace behavior and allegations of personal misconduct.
In a statement to media outlets, Brandon said he had been pondering a change for a while.
"I have been contemplating transitioning out of my role for some time," Brandon wrote. "My goal when the Pegula's purchased the franchise was to reach 20 years with the Bills in which I achieved this past November. Given where we are from a timing standpoint, particularly with the conclusion of the NFL Draft, now seems like the time to make that transition.
"As grateful as I am for the amazing experience and the incredible people I've had the privilege to work with the past two decades, I am just as anxious for the professional opportunities that lie ahead."
Brandon has been with the Bills in various roles since 1997. He became president in 2013.
He has been president of the Sabres since 2015, after the Pegulas bought the team.
Kim Pegula will take over Brandon's roles, with her husband continuing to oversee both teams' operations.
"We have a tremendous amount of confidence in the strong leadership teams we have built within each of those entities over the last several years," the Pegulas said in a statement. "We are excited about the direction of our teams, especially after this past weekend's NFL draft and NHL lottery results. Our focus remains on building championship teams on and off the field for our fans and community."
The Bills selected Wyoming quarterback Josh Allen with the seventh pick in last week's draft, hoping they have found their franchise leader.
The Sabres won the NHL draft lottery this past weekend, earning the right to draft the consensus best player, defenseman Rasmus Dahlin.
Information from The Associated Press was used in this report.