The Gers board member admits his remarks last week about the Villans' lack of competitiveness were inappropriate and has sought to build bridges with the Midlands club
The 59-year-old made the comments whilst stating his belief that the formation of a 'European League' is the way forward for the top domestic clubs on the continent.
"There will be a European league because big teams can't keep subsidising small teams for the next 10 years because they will go stale," Green had said.
"How can Manchester United's revenues be £320m and Aston Villa, who are completely useless, get £250m?"
Whilst the comments have left sections of the Villa fan base offended, a statement this week on the Rangers club website confirmed that Green has sent a letter of apology to Paul Lambert's side.
Rangers said: "Mr Green has sent an apology to Aston Villa saying there had been no intention to cause offence."