Mr Stockbridge, who has come under pressure from fans in recent months despite paying back a £200,000 bonus, has left the board with no pay off or bonus.
The Ibrox club announced the move tonight to the Stock Exchange, hours after new chief executive Graham Wallace had hinted at the move in an interview.
In a statement, it said: "Rangers announces that by mutual consent Brian Stockbridge is leaving the Company and has resigned as a director of the Company and its subsidiaries with immediate effect. Rangers confirm that no ex gratia benefit or bonus has been offered or paid to Brian Stockbridge in connection with the termination of his employment or office.
"The Directors would like to thank Brian for his contribution to the Club during a difficult period.
"The Board has commenced the search for a new Finance Director. A further announcement will be made in due course."
It comes a month after it emerged that he had been forced to return the bonus following pressure from Manx-based Laxey Partners, which plays a major role in the running of the League One club.
Mr Stockbridge had come under fire for accepting the bonus following the club's achievement in winning the third division last season.
The former finance director had been re-elected to the board at an AGM in December after seeing off an attempt to oust them led by former director Paul Murray and former chair Malcolm Murray.
The group could only achieve about 30% vote as the major of shareholders backed the current board. Mr Stockbridge's future appeared to be far from secure as he won only 65% support for re-election.
He had also faced criticism after he revealed that the club would be left with just £11million, despite a share issue that raised fortunes for the club.
He had been jeered by fans at the AGM as he revealed that there had been a £6.5m cost of setting up the the share issue which raised £22m more than a year ago.
Mr Stockbridge was part of the original team which was part of Charles Green's takeover in 2012 by Sevco. Green has also since left the club.