As reported in later editions of yesterday's Evening Times, the shares were sold for £840,000.
The buyers have been revealed as Laxey Partners Ltd, who in June this year bought 714,285 shares from Charles Green.
That amount represented 1% of the club's total available shares and with the latest purchase, Laxey Partners has increased its stake in Rangers to 4.99%.
The news was confirmed in a statement to the London Stock Exchange.
It remains unclear who sold the latest batch of two million shares, although Green is prevented from transferring any of his shares until December.
The June deal was struck last October but under the terms of a lock-in agreement, the transfer of Green's 714,285 shares to the investment firm cannot take place before December 7.
Meanwhile, Rangers have vowed to "robustly defend" any legal action taken against the club by former commercial director Imran Ahmad.
Reports suggest he is set to launch a £3.4million legal action for bonuses he says he is owed.
Ahmad left Ibrox in April - 24 hours after Rangers confirmed they were investigating reports that messages posted online were linked to his official club email account.
Ahmad was part of the Charles Green consortium which purchased the business and assets of Rangers last summer.
Green resigned as chief executive in April but has since returned as a club consultant.
Rangers finance director Brian Stockbridge said: "We are aware of this but it is without legal merit and any action will be robustly defended on behalf of the club and its fans."