The business secretary has said she "felt there was a need for new leadership" at the Post Office as it was announced its chairman is being forced out of the role.
An interim will be appointed "shortly", the Department for Business and Trade said.
Business Secretary Kemi Badenoch said: "The Post Office is rightfully under a heightened level of scrutiny at this time.
"With that in mind, I felt there was a need for new leadership, and we have parted ways with mutual consent."
Mr Staunton's departure follows frustration in Whitehall over the company's governance, including a row over the prospective appointment of a new senior independent director, Sky News reported on Saturday.
Insiders told Sky News his exit was not directly related to the Horizon scandal itself, but there had been differences of opinion between him and the government as to the best candidate for the job.
Mr Staunton had been tasked with leading the board of directors as the business reels from the fallout of what has been described as the UK's biggest miscarriage of justice.
More than 700 branch managers were prosecuted by the Post Office between 1999 and 2015 after faulty Horizon accounting software made it look as though money was missing from their shops.
Hundreds of sub-postmasters and sub-postmistresses are still awaiting compensation despite the government announcing those who have had convictions quashed are eligible for £600,000 payouts.
Call for 'major change' in senior management
Labour MP Kevan Jones told Sky News the government needed to explain why it had sacked Mr Staunton, adding: "I would also argue that there needs to be major changes in the senior management of the Post Office.
"Remember, on his watch, the senior executives who got bonuses for cooperation with the public inquiry, even though the public inquiry is still trying to get information out of the Post Office. So no, there's more changes got to happen."
Mr Jones also said there "should be a serious question mark" over Post Office boss Nick Reed's position.
Tory peer Lord Arbuthnot, who has sought justice for the sub-postmasters and sub-postmistresses, ruled himself out of the running to replace Mr Staunton.
"There is a need for dramatic cultural and governance change which can be brought in only by someone with experience of doing that sort of thing," he told The Independent.
Business Secretary Kemi Badenoch will appear on today's Sunday Morning with Trevor Phillips, which starts at 8.30am.