Rangers announced via the stock exchange that major shareholder Laxey had transferred the credit facility to George Letham, who had made a public offer to the club in the wake of criticism of the original deal.
Laxey stood to make £150,000 on the six-month loan while a combined £1.5million loan from the hedge fund and football club chairman Sandy Easdale was secured against the Edmiston House and Albion car park properties adjacent to Ibrox Stadium.
But Letham will now loan the club £1million in return from a smaller premium.
A statement from Rangers' plc read: "On 24 February 2014, the company announced that it had entered into two secured short term credit facilities for an aggregate amount of up to £1.5 million. These credit facilities were provided by Laxey Partners Ltd to the amount of £1 million and Alexander Easdale to the amount of £500,000.
"Laxey has, pursuant to an agreement entered into today, transferred all rights and obligations in relation to the Laxey Facility to Mr George Letham including all its rights in relation to the standard security granted as security for the Laxey Facility. Mr Letham is a shareholder in the company and a lifelong Rangers fan.
"The Laxey Facility, now transferred by Laxey to Mr George Letham, remains subject to the same terms and conditions with the exception that the premium payment has been reduced to £45,000 and remains payable in shares or cash."
Letham previously stated that he only wished to receive extra shares in return for his loan.
Quoted on the Rangers Standard website, he said: "'It is my intention to convert this interest into shares as I have no wish to take cash out of the club. If the club are unable to convert the interest to shares, then any cash sum I received from the loan would be reinvested into the club via a future share issue to further the cause of fan ownership.
''My only motivation in this is to ensure that the club is secure, has as much involvement as possible from those who care about it and that its vital assets remain available to it at all times."
While the loan will see Rangers through a short-term cash shortage, questions remain over their long-term financial strength.
Former Ibrox director Dave King, who lost his £20million investment when oldco Rangers were consigned to liquidation, this week claimed the club needed £30-50million fresh investment to be able to compete with Celtic - and he is prepared to underwrite a fresh share issue.
South Africa-based King is awaiting the outcome of chief executive Graham Wallace's 120-day review of the club's finances and operations but Rangers fans have called on the board to signal how they will go about bolstering the team.
A statement from the Union of Fans, which reprsents all of the main Rangers fans' groups, read: "It was clear from our discussions with him last week that the £30m+ Mr King is willing to invest is crucial to take the club back to a competitive level and improve the infrastructure and facilities. The club has been neglected, that cannot continue.
"Only once this investment has been made will Rangers be able to live within its means, something we all want for the longer term future.
"We would now ask the board to indicate publicly, as a matter of urgency, whether they are prepared to accept Dave King's offer of massive investment. The ball is firmly with the Rangers PLC board, in particular with chief executive officer Graham Wallace and chairman David Somers.
"Dave King has put a figure on what Rangers need and has shown his commitment to, and ambition for, the club he has supported all his life. Do Mr Wallace and Mr Somers agree with his figures and if they do, how do they propose to raise this large sum of money without Dave King?"
Meanwhile, Rangers have signed former Hamilton right-back Ryan Finnie for their under-20s team until the end of the season. The 19-year-old made five first-team appearances for Accies before leaving in January.