The Ibrox chief executive reaffirmed his commitment to the Glasgow giants after a Walter Smith-led consortium withdrew their interest in buying the club.
The former Light Blues boss revealed plans for an 11th-hour bid last Thursday, just before Green and his investors completed the purchase of the business and assets of Rangers as a newco.
Smith's group have since failed with a £6million offer and rejected the opportunity to join Green's consortium, before agreeing to step aside. Former Sheffield United chief executive Green is now keen to look to the future.
He said: "I fully recognise there is a huge job to be done to rebuild the trust between the fans and the club which has been badly broken."
Green continued: "I will do everything I can to help rebuild Rangers and the most important challenges we face at the moment are about our future and what league we play in.
"I can assure fans that I will work tirelessly in the interests of the club to secure its future."
Malcolm Murray, chairman of The Rangers Football Club, said: "The consortium is wholly committed to rebuilding Rangers and their investment is regarded as a strategic long-term project.
"As I have said previously I am not in this for personal gain and what is of paramount importance is the club regains stability both in financial and footballing terms.
Since the announcement last week by the Walter Smith consortium, our position as a board has been clear in that we would welcome constructive dialogue with all those involved.
"The Green consortium said last Thursday evening that it was not looking for a sale and that is the view of the investors. We can however say to supporters that the assurances the Walter Smith consortium are looking for regarding financial probity and high standards of corporate governance will be met.
"Following the announcement on behalf of the Walter Smith consortium, the board would urge all Rangers fans to now get behind the club."
Two-times manager Smith was willing to step aside after receiving "verbal assurances" from the new regime.
He said in a statement: "We are withdrawing completely from the process to enable Charles Green and his consortium to move forward.
"We very much hope the verbal assurances they provided to us - and the public statements made - are adhered to and that the club will therefore be financed and managed with appropriate governance and can go forward in a sustainable manner.
"We wish the new Rangers Football Club every good fortune."