Green tendered his resignation as chief executive on Friday following a number of claims surrounding his dealings with former owner Whyte before his consortium took control at Ibrox in June last year.
International law firm Pinsent Masons will work in conjunction with financial experts from Deloitte.
A club statement read: "Rangers International Football Club plc ("Rangers") has instructed the law firm Pinsent Masons, supported by forensic investigators from Deloitte, to investigate the connections between Craig Whyte and former and current personnel of Rangers and its subsidiaries."
Rangers earlier issued a separate statement to the London Stock Exchange announcing that Sevco 5088 - the company at the centre of a dispute between Green and Whyte - was a subsidiary of the club at the time of their flotation on the stock exchange.
The statement added that Green was a director of Sevco 5088, which was used to buy the assets and business of the liquidation-bound club in May last year.
Whyte claims he was behind the firm and has threatened legal action arguing he is the rightful owner of Ibrox and other club assets.
The assets were transferred to another new company, Sevco Scotland, days after the £5.5million purchase in June last year, when the club was consigned to liquidation over tax debts accrued during Whyte's tenure.
This new company became The Rangers football Club Ltd, which is owned by holding company Rangers International Football Club PLC, which was floated on the AIM division of the London Stock Exchange in December.
Green tendered his resignation on Friday days after the club board announced an independent report into the allegations over the extent of his association with Whyte.
In a statement released by the club on April 5, Green said: "In a discussion with Mr Whyte, who taped some conversations, I am alleged to have said: 'You are Sevco, that's what we are saying'.
"This is correct but at that point I had signed a resignation letter and a stock transfer form because it was decided that a Scottish company should buy a Scottish institution. Sevco 5088 wasn't required."
There was no announcement today over the appointment of an interim replacement for Green, who stepped down with immediate effect.
Reports have claimed that Craig Mather, a major investor who was brought on board by Green in the early stages of the new company, is favoured by some directors to take over on an interim basis.
Another director, Phil Cartmell, who is chairman of Slough-based engineering firm Corac, is said to be close to leaving the board.