The chief executive told fans groups this week he plans to remain at Ibrox until his retirement, unless he is removed from the board by supporters.
It was initially expected that Green would remain at Rangers only on a short-term basis to make money after his consortium purchased the business and assets of the club when liquidation was confirmed.
However, he now appears ready to make a more solid commitment to the Light Blues, a move which has been welcomed by McCoist.
He said: "I can't speak for Charles but, when he first came in, he was very up-front and honest and said he was only here for a short period of time.
"He wanted to get the club back on an even keel, back moving forward again, and obviously make a bit of money - and that's fair to be honest with you.
"From where I'm sitting, it looks as though he has appreciated the support and, maybe not underestimated the size of the club, but now fully appreciates the size of the club, the people within the club and, indeed, the support and he is enjoying being part of it.
"That's why, I think, he has pledged his longer term future to the club and the fans."
Green, 59, indicated he could remain at Rangers for another 10 years.
McCoist added: "It's really encouraging. I think he actually said he was staying until he was 70, which is a heck of a statement.
"I think what Charles was doing was pledging his future to the club because he believes there is a lot of work to be done, like the rest of us.
"It's important that the fans, who have been fantastic, are sent the right message.
"Everybody knows there is a lot of work to be done and we want to get the work done."
Green is in talks with several parties, including Rangers shareholder and Newcastle owner Mike Ashley's Sports Direct firm, over the sale of stadium naming rights, albeit he is keen to retain Ibrox in any new title.
McCoist said: "I know Charles has met a lot of fan groups in the last week or so and their opinions have been taken on board.
"I still remain pretty open-minded about it.
"There is the traditionalist in me, of course there is, who wouldn't like to see anything change.
"At the same time, we have to move forward and we have to change.
"There is nothing agreed yet but, if there was a change, I would certainly expect and hope Ibrox to be involved in it (the name)."
Green also told fans talks are ongoing with Ashley over an agreement that could see Rangers buy or loan Newcastle players in the future.
McCoist said: "I would be delighted, as long as the traffic is one way.
"Any opportunity we can look at to bring a better quality of player in and bolster the squad and help the players who are here, we would certainly be very welcome to."
Rangers play host to Montrose in the Irn-Bru Third Division tomorrow and McCoist warned against a repeat of the 1-1 draw with Elgin City at Ibrox earlier this month.
He said: "It's another opportunity for us to take three points but we will have to work really hard for it.
"The fact that we took our eye off the ball a little bit in the last five minutes against Elgin, and paid the price for it, is certainly a reminder to everybody that we have to keep going for the 90 minutes and we have to work hard to get our victories at home and away."