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Mark Taber, Andrew Clayton and Gene Schneur will become new board members, with Patrick Stewart remaining as chief executive.
Current board members Fraser Thornton, John Halsted and George Taylor will stay on as Graeme Park, Julian Wolhardt and Alastair Johnston step down.
“We are deeply grateful for the trust placed in us by the Rangers board, shareholders, staff, and supporters,” Cavenagh said.
“This club’s history and traditions speak for themselves, but history doesn’t win matches. We know that the true way to honour the club’s heritage will be to drive performance.
“Our focus is simple: elevate performance, deliver results, and bring Rangers back to where it belongs – at the top.”
Cavenagh and Marathe, president of 49ers Enterprises, “will oversee all aspects of the club” with new sporting director Kevin Thelwell officially starting his role on Monday.
Rangers are in the final stages of their search for a new manager, with departing Real Madrid assistant Davide Ancelotti and former Southampton boss Russell Martin understood to be the leading candidates.
“At 49ers Enterprises, we have built a track record of sporting and business success, but our driving motivation is our deep connection to the clubs and communities we serve,” said Marathe.
“We are excited to join Andrew and our other consortium of investors in a new era for this iconic club, and we are determined to build something that supporters can be proud of for years to come.”
Chief executive Stewart said: “From my earliest conversations with Paraag and Andrew, I have been excited and confident in the shared vision and what it could mean for the future of Rangers.”
Thornton added: “I also want to acknowledge our major shareholders whose backing has brought the club to this point, the vast majority of whom have chosen to reinvest in the club and continue with us on the next stage of the journey.”