Sam Allardyce says he is “deeply disappointed” to have left his role as England manager after just 67 days.
It came after a newspaper reported he had offered advice on how to “get around” player transfer rules.
Allardyce made a “wholehearted apology” and said he recognised some of his comments had “caused embarrassment”.
The FA called his conduct inappropriate and said his contract was ended by mutual agreement. Gareth Southgate will be in charge for four England matches.
Allardyce was filmed by undercover reporters from the Daily Telegraph, who posed as businessmen for a meeting in which he reportedly said it was “not a problem” to bypass rules on third-party player ownership, and claimed he knew of agents who were “doing it all the time”.
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It was also claimed that a £400,000 deal was struck for him to represent the company to Far East investors and to be a keynote speaker at events.
Allardyce also referred to his Roy Hodgson as “Woy”, making fun of his predecessor’s manner of speaking, and criticised Gary Neville, one of Hodgson’s assistants.
Further details of the Telegraph’s wide-ranging investigation are published in Wednesday’s edition of the paper – including a claim that eight past and present Premier League managers have been accused of receiving illicit payments for transfers.
Five of the unnamed eight have denied the allegations while three are yet to comment, the paper says.
In a statement on the FA website, Allardyce said it had been “a great honour” to be appointed England manager and that he was “deeply disappointed at this outcome”.
“Although it was made clear during the recorded conversations that any proposed arrangements would need the FA’s full approval, I recognise I made some comments which have caused embarrassment,” he said.
“As part of the meeting, I was asked to clarify what I said and the context in which the conversations took place. I have co-operated fully in this regard.
“I also regret my comments with regard to other individuals.”
FA chief executive Martin Glenn said Allardyce was “distraught” to have left his role.
“He recognises that he made a terrible error of judgement,” he said.
“Sam understands why the FA has had to take this tough decision.”
The FA said it would begin its search for a new England manager while Southgate takes charge for the matches against Malta, Slovenia, Scotland and Spain.
Allardyce succeeded Hodgson in July following England’s disastrous performance at Euro 2016 in France.
After just one match in charge – a 1-0 win over Slovakia in England’s opening World Cup 2018 qualifier – he becomes the national side’s shortest-serving full-time manager.
BBC Sport chief football writer Phil McNulty
Sam Allardyce never made a secret of his desire and suitability to be England manager – so he will be heartbroken that the dream he harboured throughout his career is over in 67 days.
The Football Association will be equally dismayed at being plunged into uncertainty so soon after appointing the man it believed would signpost a bright future towards the World Cup in two years after the debacle of Euro 2016.
Sadly for Allardyce, the lack of judgement and loose-tongued approach that saw him caught in a Daily Telegraph sting meant events at Wembley on Tuesday were always heading towards an inevitable conclusion.
Some may have sympathy for Allardyce, gone after one victory in Slovakia and brought down by non-footballing matters, but the FA’s statement spoke of the need for strong leadership and respect for the integrity of the game, and it clearly felt his behaviour was unbecoming of an England manager.
|England’s shortest serving full-time managers (and the longest)|
|Name||Games in charge||Time in charge|
|Sam Allardyce||1 (2016)||67 days|
|Steve McClaren||18 (2007-2007)||One year, six months, 18 days|
|Kevin Keegan||18 (1999-2000)||One year, seven months, 17 days|
|Terry Venables||23 (1994-1996)||Two years, four months, 29 days|
|Glenn Hoddle||28 (1996-1999)||Two years, nine months|
|Don Revie||29 (1974-1977)||Three years, seven days|
|Walter Winterbottom||139 (1946-1962)||18 years|
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