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."
- Sports & Recreation