The Ibrox club confirmed the finance director's departure last night - and insisted he had been given no pay-off. But he is leaving with a full year's salary - £200,000.
Mr Stockbridge had previously been forced to hand back a £200,000 bonus after an ultimatum by the club's biggest shareholder.
The 40-year-old has been repeatedly slammed by fans over the precarious financial state of the club.
It is understood his departure is part of chief executive Graham Wallace's "restructuring" of the club.
The departure was immediately welcomed by Drew Roberton, general secretary of the Rangers Supporters' Association. He said: "I think it's a good thing for the club.
"I think it's Graham Wallace sending out a message that he's the boss and he's not afraid to take big decisions. It gives fans some encouragement.
"I'm not disappointed to see Stockbridge go. He just didn't do much to endear himself to anyone. We've got to hope Mr Wallace is starting as he means to go on."
In a statement to the London Stock Exchange, the club 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."
Many fans expressed surprise he stayed in his position with the club after its crucial AGM last month.
His close links with controversial duo Charles Green, the club's former chief executive, and Imran Ahmad, an ex-director, caused concern for fans.
The club is operating at a loss and Mr Stockbridge previously said there would be only £1million left in the bank by April.
Investment group Laxey Partners said it would only support Mr Stockbridge's re-election at the AGM if he repaid his £200,000 bonus, which he accepted for Rangers winning last season's third division title.