Steve McClaren was sacked as England manager on Thursday following their failure to qualify for the European Championship finals next year.
At a news conference at Soho Square, the FA said they had made a unanimous decision to terminate the contract of McClaren and his assistant Terry Venables at a meeting this morning.
And the FA's chief executive Brian Barwick made a personal apology to England fans for the team's failure to qualify for Euro 2008, while the chairman Geoff Thompson said it was embarrassing.
As bookmakers made former Chelsea boss Jose Mourinho the favourite for the job, Barwick added that the nationality of England's next coach will not be an issue.
McClaren's time in office - at just 18 games the shortest tenure of any coach in the post - came to a humiliating end last night with a 3-2 defeat to Croatia at Wembley which ended England's hopes of reaching next summer's tournament.
FA chairman Geoff Thompson said: 'At a meeting of the FA board this morning the FA board unanimously decided to terminate the contract of England head coach Steve McClaren with immediate effect.
'We have also terminated the contract of assistant Terry Venables.'
McClaren refused to resign immediately after the game, but it appeared only a matter of time before he was axed.
All the major FA powerbrokers were at Soho Square for the meeting, and the speed with which they arranged a press conference suggested McClaren's future was not even a matter of debate.
Thompson continued: 'The recruitment process begins now, and we will do everything we can to get the right man for the job.'
Barwick admitted McClaren's failure to qualify for Euro 2008 cost him his job.
He said: 'It was a board decision - it was unanimous.
'I spoke to Steve this morning - we get on very well with him. I've had many grown-up conversations and had another one with him this morning - and I can only wish him well.
'But in the end, not qualifying for Euro 2008 comes up short. Qualification for a major tournament is probably a minimum requirement.'
Barwick admitted the task of finding a new manager would be handled differently to the last appointment.
'The recruitment process for the new coach begins now and we will do everything to get the right man for the job,' he said.
'It will be done differently. We've got to learn lessons from the way we did it.'
Pressed on whether there will be a change in the appointment process after pressure was brought to bring in an Englishman following Sven-Goran Eriksson's exit, Barwick made it clear all candidates will be considered.
'I don't think nationality will be an issue,' he said.
Thompson admitted the failure to qualify was embarrassing to the governing body.
'Of course we feel embarrassed,' he said.
'As we said earlier we expect as a major nation in Europe to qualify for the European Championships and World Cups. Of course we're embarrassed, disappointed, disappointed like all fans.'
Barwick was similarly humbled and offered a heartfelt apology for the situation: 'I'd like to apologise to the fans personally.
'I care about this passionately, it has never been just a job. I'm in it because I care about football, football fans and football teams.
'Last night was a tough, tough night.
'We care about this very much. I understand we have let them down and apologise for that.'
Asked about the financial loss, Barwick said: 'To the FA, less than £5million.'
Barwick also denied he regretted giving McClaren a four-year contract.
'The contract is a private contract. I don't regret that now; I think he has tried very hard.'
Board director and Premier League chairman Sir Dave Richards defended Barwick, saying: 'Brian has taken a lot of stick about him being the sole person (to appoint McClaren).
'This responsibility has to be shared among us all. It's unfair to say he was Brian's man - he was the FA's man.'
On the issue of the number of overseas players in the top flight, Richards added: 'You would know as well as anybody that the Premier League is the best in the world, because it has the best stars in the world.
'There are also rules in the European Union that allow players to come, and clubs will pick the best stars.'