The McGill's Buses owner has confirmed that he has finally concluded a "binding agreement" to purchase the former Light Blues chief executive's shareholding following a deal originally struck in May.
Green was the man who led the consortium which purchased the business and assets of Rangers for £5.5million last summer, after the club was consigned to liquidation.
He owned 714,285 shares in the former Scottish champions - around 7.7% of the total shareholding.
Now Easdale - whose brother James is a Rangers director - claims the honour belongs to him, while Green says his association with the club is now at an end.
In a statement to Press Association Sport, Sandy Easdale - who runs his various business interests alongside brother James - said: "There has been continued speculation and constant enquiries to buy this largest holding in Rangers but Mr Green gave me the first option which I exercised. Between my family holdings and through other supporting investors I now have the largest shareholding in Rangers Football Club."
This latest development comes amid an increasingly bitter boardroom dispute at Ibrox.
Shareholder Jim McColl is leading a call for chief executive Craig Mather and his fellow directors Brian Stockbridge and Bryan Smart to be removed from the board and replaced by former Ibrox director Paul Murray and accountancy expert Frank Blin.
A spokesman for Sandy Easdale added: "Sandy's only interest is to see peace brokered at the club. He felt he should increase his financial commitment to the club while sending a message to those who want to grab power at Rangers without investing a brass farthing."
The spokesman also confirmed that the agreement struck with Green would see Sandy Easdale take control of the "vast majority" of the Yorkshireman's shares.
The rest - described as a "small amount" - are due to go to Isle of Man-based investment firm Laxey Partners following a deal struck in June.
In a statement, Green added: "Over the last few months numerous individuals and corporate bodies have expressed interest in obtaining my shares although much of this was to solicit press coverage and attract attention. Sandy said he would buy them and he has. I knew he would and he will do what's best for Rangers now he has a more substantial percentage.
"I want to make it clear that this means I will have no ongoing influence or financial interest at the club but I remain a fan and fervently hope that Rangers will soon be back at the top where they belong."
Green returned to Ibrox as a £1,000-a-month consultant last month but was forced to step down just three weeks later after a supporter backlash.
His outspoken spell as chief executive ended in April when he resigned amid allegations of links to former Rangers owner Craig Whyte, who put the club into administration 18 months ago.
Former director Imran Ahmad has launched a £3.4million legal action against the Glasgow club but fans were angered when he revealed he had Green's backing for the claim.
Green's return as a consultant was designed to placate some of the club's investors as Rangers' share price dropped to just 41 pence.
But he sparked controversy when he claimed first-team boss Ally McCoist would have a "problem" if he failed to lead the team to a domestic cup win this term.
McCoist hit back by labelling him an "embarrassment" to the club and Green finally stepped down on August 2 after Mather called a board meeting to discuss firing him from his latest role.