Effective following an extraordinary general meeting of the Rangers board on 6 March, Bennett was appointed alongside Rangers Supporters Trust member Chris Graham.
Henderson confirmed that Bennett, director of European equity, will retain his duties at the head of the firm’s European fund range.
Paul Murrary, Rangers interim chairman, said: “We are delighted to announce the further strengthening of the RIFC board following Friday’s general meeting.
“John’s corporate and financial experience and track record will prove invaluable.”
The Ibrox club has endured a tumultuous period since entering administration in 2012 and being forced to apply for re-admission to the Scottish Football League’s bottom tier as a new company.
Bennett, a life-long Rangers fan, has been a member of the Blue Knights supporters’ group since March of that year, and has previously voiced his belief that fans should have “a major say” in the running of the club.
Rangers has drawn the attention of several high-profile investors during its climb back to the top of Scottish football, including Sports Direct CEO Mike Ashley, and counts River and Mercantile among its largest stakeholders.