Rangers, champions a record 54 times, must now ask other Scottish Premier League (SPL) clubs to allow them to remain in the top flight after their debt-laden parent company was liquidated.
"The consortium I represent has fulfilled its agreement with the administrators and has completed the acquisition of the business and assets of Rangers Football Club plc," Green said in a statement.
"Our consortium wants Ally McCoist to remain as manager and we firmly believe he is the man to take Rangers forward," said Green who was previously involved in the sport as chief executive of English second-tier Sheffield United.
There was another twist in a convoluted tale earlier on Thursday when former Rangers manager Walter Smith said he was leading a group of Scottish businessmen who wanted to take over the club and urged Green to drop his deal.
McCoist played under Smith in the 1990s and was also his assistant manager before taking the top job last year.
Smith's intervention appears to have come too late to affect the takeover but it could make it harder for the new owners to win over the Rangers fans.
Green gave details of the new investors in the club and they include Scottish clothing company Glenmuir.
UNPAID TAXES
Rangers, one of the biggest teams in British football, went into administration in February over unpaid taxes of around nine million pounds.
They also faced a much bigger potential tax liability relating to how they paid their players over the past decade.
The tax authorities rejected a settlement with Green earlier this week, consigning the club to liquidation and raising questions about which league the reformed Rangers should play in next season.
Officials said their decision would ensure a proper investigation into what went wrong at Rangers and should help to recover more of the money taxpayers were owed.
The new owners have said the club will remain at their iconic Ibrox home.
Rangers and Celtic have dominated for decades and the bitter rivalry of the two Glasgow clubs is an integral part of the game in Scotland.
"An application has already been made by the company to register with the Scottish Football Association and to participate in the SPL," Green said.
"These applications will be considered over the next few weeks and I will continue to have discussions with the football authorities in relation to the club's position."
The issue is pressing as the SPL fixtures are due to be announced on Monday, with the new season starting on August 4.
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