The body said in a statement that Browning, appointed in February, had announced at a board meeting on Wednesday that he was leaving on 1 December.
It said this was “in compliance with the new Code for Sports Governance which requires a new independent chair to be appointed”.
Browning has withdrawn his candidacy for that role and will resume his previous role of non-executive director.
Cycling is one of Britain’s most successful and heavily funded sports, enjoying huge success at the Olympic and Paralympic Games.
But British Cycling was heavily criticized for “a culture of fear” in an independent review published in June that found failings in governance and leadership.
It has also been at the centre of an investigation by UK Anti-Doping into allegations of wrongdoing.
“I have a passion to see through the transformation that we started, and have been encouraged by others to continue this work, which is why I put myself forward as a candidate for the role of independent chair,” said Browning.
“However as I went through the process, it became clearer to me that British Cycling would benefit from a new leader to see it through the next stage of its development.”