Mr Stockbridge, who was part of Charles Green's Sevco consortium that bought the assets of the former Rangers club from liquidation in 2012, is to get the one-off payment because he is quitting before the end of his contract. It flies in the face of a club statement to the London Stock Exchange, issued last night, which insisted he would receive neither a bonus nor severance pay.
Rangers 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."
The decision, which sources close to the club insist was taken by new chief executive Graham Wallace rather than by mutual consent, is being seen as the parting shot in a major reshuffle.
Philip Nash, the former Liverpool and Arsenal finance chief recently appointed to the Rangers board, will take over on an interim basis from Mr Stockbridge, but is favourite to get the job.
Mr Stockbridge came under heavy criticism from shareholders at the club's AGM in December after the League One club reported a £14 million operating loss for the 13 months to June.
He was re-elected to the board with support from just 65.3% of shareholders, the smallest margin of any of the five board members.
His departure will appease fans who were unhappy with Mr Stockbridge's continued presence at the club.
He recently paid back a £200,000 bonus that he had been awarded after Rangers won the third division last season.
Mr Stockbridge admitted he was not at the club "to win a popularity contest".
Derek Roberton, general secretary of the Rangers Supporters' Association, said: "I'm not disappointed to see him go.
"He just didn't do much to endear himself to anyone. It's not so much what people think about his responsibility for the financial health of the club, but it was his demeanour - I'm not sure if condescending is the word, but we requested meetings with him and he was very dismissive.
"That's okay when you're behind closed doors on the board of any other company to act like 'I'm not here to make friends with anybody', but when you're on the board of a football team like Rangers you've got 50,000 people to make friends with.
"We've got to hope that Mr Wallace is starting as he means to go on."