An extraordinary general meeting of 'oldco' shareholders took place at Ibrox on Tuesday, where procedures were approved to enable the name change.
Charles Green's Sevco consortium completed the purchase of the business and assets of Rangers in June after the club was consigned to liquidation following failure to secure a Company Voluntary Arrangement in order to exit administration.
The Glasgow giants - who will play in the Irn-Bru Third Division this season - began a new chapter in the club's history on Sunday when they faced Brechin in the Ramsdens Cup in their first competitive outing since the change of ownership.
They were granted conditional Scottish Football Association membership on Friday night, which will be completed when the formal transfer of 'oldco' Rangers' Scottish Premier League share to Dundee takes place later this week.
Green told www.rangers.co.uk: "The process that took place today is the penultimate piece of the jigsaw that will see The Rangers Football Club move forward, with the transfer of SFA membership being the final piece.
"As every fan knows, Rangers is Rangers - it always has been and it always will be.
"The club still has its 140 years of history and we are now embarking on the next 140 years.
"We are back playing football and the board is focused on rebuilding this great club over the next few years.
"Our fans were fantastic on Sunday at Brechin and their support at Ibrox and away from home this season will be instrumental in helping the team achieve the success we all desire."