"They result from John McClelland and John Greig both being of the opinion that since the change of ownership they have been excluded from participating in corporate governance at the club.
"Therefore they have decided not to continue in their positions as non-executive directors."
Greig, who made more than 750 appearances for Rangers following his debut in 1961, joined the board on Boxing Day 2003 having returned to the club as public relations officer in 1990, seven years after quitting as manager.
McClelland has been on the board since 2000, and enjoyed a spell as chairman from 2002 to 2004 when Sir David Murray temporarily stepped down from the post.
The pair were on the independent board committee, which delayed Whyte's buyout and then expressed concern over "a lack of clarity" over the new owner's financial muscle, hours after he had completed his buyout of Murray's shareholding on May 6.
The committee was led by chairman Alistair Johnston, who was removed from the board later in May, along with Paul Murray, who had launched a rival takeover deal.
McIntyre, who remains an employee of the club, and former chief executive Martin Bain were suspended the following day. Both have launched legal actions against Rangers.
Donald Muir and Mike McGill left the board on the day Whyte took over.
The board now comprises of chairman Whyte along with King, chief operations officer Ali Russell, director of football Gordon Smith and non-executive director Phil Betts.
The Scottish champions, who are involved in two separate tax disputes with HM Revenue and Customs, today refused to comment other than to say the resignations had been accepted.