Roy Hodgson resigned as England manager after his side suffered a shock 2-1 defeat by Iceland to crash out of Euro 2016 at the last-16 stage.
The 68-year-old had been in charge for four years after replacing Italian Fabio Capello but has won just three of 11 games in major tournament finals.
Iceland - with a population of just 330,000 - were among the lowest-ranked teams in France at 34 in the world.
"I'm sorry it will have to end this way but these things happen," Hodgson said.
"Now is the time for someone else to oversee the progress of a hungry and extremely talented group of players.
"They have done fantastically and done everything asked of them. I hope you will still be able to see an England team in a final of a major tournament soon."
Hodgson, who won 33 of his 56 games as England boss, would have been out of contract at the end of the tournament.
The former Liverpool and West Brom boss was due to discuss a possible contract renewal but Football Association chairman Greg Dyke said he would only stay on if England "do well" in France.
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