The Govan club's record goalscorer and current manager confirmed he has backed with his own money chief executive
Green claims to have raised £17 million ($26.11 million) of institutional investment and has ring-fenced £10 million ($15.36 million) worth of shares for fans who have until Tuesday lunchtime (local time) to sign up.
McCoist is already listed in the share offer prospectus as owning 1 million shares in the club, a stake of just under 3 per cent.
The brochure goes on to state that he will have more than 70,000 more shares after the new shares are issued but a smaller stakeholding of less than 2 per cent.
Ahead of Tuesday evening's (Wednesday morning AEDT) Third Division game against Annan Athletic at Ibrox, the former Rangers striker revealed he has given Green's plans for the future of Rangers a 'vote of confidence'.
"I have personally invested in the club," said McCoist.
"I think the best way to put it is that I have bought shares in the club as a fan, I haven't bought them specifically as the manager.
"I wanted to do it as a supporter and when I am long gone the shares I have invested in the club will be passed down in my family.
"It is obviously close to my heart and like a lot of Rangers supporters will do, I did it on behalf of my family, it's not so much for myself, more for my sons than anything else.
"I have been incredibly boosted by the level of support shown by the fans.
"In the rebuilding process that we are all part of - and it is the early stages - I wanted to give my own vote of confidence if you like, in buying shares in the club.
"As I say it is something a lot of Rangers fans will do for their own families, hopefully, and being one of them I felt it was something I wanted to do.
"The long-term future of the club is of paramount importance and we are going to do that with the support and help of people around the club.
"We have plans and agendas for the future and it will be determined by level of support shown from supporters and indeed other people."
A battling 4-2 win over Montrose kept Rangers at the top of the table and McCoist believes that his side, now into its second round of fixtures against its Third Division rivals, is getting used to life in the fourth tier of Scottish football.
"I think the novelty factor has perhaps worn off a little bit for the opposition," he said.
"I am hoping that's the case, although I am contradicting myself because at the weekend Montrose looked a different proposition than they did at our place.
"They were well up for it and really gave us a game.
"That said, I am hoping our players know what to expect now in terms of the opposition and the competition.
"And I don't want to tempt fate but that type of game at the weekend, we might not have won at the beginning of the season away from home.
"We are getting to know each other and I am just hopeful that the players are developing a toughness and a winning attitude which is very important.
"Annan will be boosted by the fact that they gave us a proper game at their place when there were no goals.
"I am just hopeful that we are a different proposition at home than we were down there."