Last season's runners-up have so far sold 45,757 briefs, beating 45,419 from the previous campaign.
Impressively, nearly 14,000 fans are on the waiting list.
King paid tribute to the club's supporters and called Rangers "the country’s premier club".
“Once again Rangers supporters have stepped forward and reminded us that we, the directors of this special club, are in a fortunate and privileged position to be able to work for them and with them," he said.
“The loyalty shown by Rangers fans towards their club never ceases to amaze me and, on behalf of my fellow board members, I again express my gratitude and admiration.
“Rangers has always been a leader on and off the pitch and with the support that our fans continue to demonstrate we will maintain that tradition.
“I have said before, but it is worth repeating, that Rangers is special and, having won more trophies than any other club in the world, we have a genuinely unique place in football history. We must keep it that way while welcoming everyone who wants to be part of this wonderful institution.
“This is an inclusive and diverse club and we are close to announcing initiatives which will make Rangers even more special to so many more people.
“I said recently that it would be remarkable if we could get to last season’s figure for season ticket sales but you have done more than that.
“You have set a new high and I am immensely proud to be chairman of this great club. Let’s continue to do the right things and project Rangers as the country’s premier club and again, thank you for your wonderful support.”
The club are currently in the Algarve for a pre-season camp. Joe Aribo is set to become the seventh signing of the season.