The group, which is being led by wealthy Scottish businessman Jim McColl, had called for chief executive Craig Mather and directors Bryan Smart and Brian Stockbridge to stand down.
They wanted former Price WaterhouseCoopers accountant Frank Blin and ex-director Paul Murray appointed in their place.
But in a statement to the London Stock Exchange the Glasgow club confirmed the group had withdrawn the requisition.
The club said: "The company confirms that all of the current directors remain in office and that it is not appointing any additional directors save that as previously announced, the company confirms that it continues to actively seek to appoint a new chairman."
Discussions between the club board and the disgruntled shareholders have been ongoing since the move to have directors replaced was made.
An agreement had to be reached before today or the club would have been forced to convene a general meeting before the annual meeting due to take place in October in order to settle the disagreement.
Rangers announced earlier this month that the board would consider a request for Blin, Murray, former chairman John McClelland and Greenock businessman Sandy Easdale to be added to the board.