The club confirmed Stockbridge's departure in a brief statement to the London Stock Exchange and insisted he had been given no pay-off.
The statement read: "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."