The Hayes Lane boss took over in 2016 and his five years at the helm are over, it has been confirmed.
Bromley are sitting in seventh place in the National League table, but lost 3-1 at home to Sutton United on Tuesday night.
The club say their search for a new manager begins immediately.
Chairman Robin Stanton-Gleaves outlined the reasons behind the decision.
He told the club’s website: “This has been a difficult decision to make and one that has not been taken lightly.
“Having continued to review first team performances and developments over an extended period of time, I now believe a change in leadership is required for us to progress further on our journey.”
“Neil has undoubtedly played an integral part in pushing the club forward both on and off the pitch.
“He has given Academy scholars first team opportunities and his work within our community on bringing players and supporters closer together has been invaluable. I know supporters will never forget him guiding us to an appearance at Wembley Stadium for the first time since 1949, in an FA Trophy final.”
He added: “He has had my full respect and support during my Chairmanship and I’d like to take this opportunity on behalf of everyone at Bromley Football Club to place on record our sincere thanks to Neil for all the work he has done during his near decade with the Club and wish him all the very best for the future.”
Bromley will update supporters on an interim replacement “in due course”.