Coaches Ray Lewington and Gary Neville will also leave their posts to make way for a new regime to take the team on to the 2018 World Cup in Russia.
Hodgson said: “I’m extremely disappointed of course about tonight’s result and ultimately our exit from the competition.
“I’m actually proud of the work my coaching staff and I have achieved over our time at the helm of England. The transition from the squad whose average age was 30 to now being the youngest in the tournament is both remarkable and exciting for the future of English football.
“I would have loved to stay on for another two years. However, I am pragmatic and I know we are in the results business. My contract was always up after the Euros, so now is the time for someone else to oversee the progress of this young, hungry and extremely talented group of players.
“They have been fantastic and have done everything that has been asked of them. When I arrived I was told players didn’t turn up to play for their country or that they pulled out at the last minute. I have not seen any of that. These players love to play for their country and their commitment has been unquestioned.
“Ray and Gary arrived with me as part of my coaching team and will leave with me. I’d like to thank them for their dedicated support and for the major part they’ve played in our team preparation.
“Finally I’d like to thank all the support start, players, the FA and of course the fans. It’s been a fantastic journey, these four years, and it’s one I’ll look back on or remember with pride.
“I’m sorry it’s had to end this way with another exit from the tournament. These things happen. All I can do is wish everybody all the very best and hope that you will still be able to see an England team in a final of a major tournament fairly soon. We’ve been unable to deliver.”
FA said: “Like the nation, we are disappointed to lose this evening and that our run in Euro 2016 has come to a premature end. We had high hopes of progressing through to the latter stages of the competition and accept that we have not met our own expectations or those of the country.
“We back Roy Hodgson’s decision to step down as England manager and will discuss next steps imminently.
“For now, we congratulate Iceland for reaching the quarter final and wish them well against France at the weekend.
“Finally, our sincere thanks go to the travelling fans for their incredible support tonight and to everyone back home for getting behind the team.”
Hodgson, out of contract at the end of the tournament, won 33 of his 56 games in charge of England.
He guided the team to the quarter-finals of Euro 2012, where the Three Lions lost to Italy on penalties, before overseeing the disastrous 2014 World Cup campaign where they were knocked out at the group stages.
England took the lead against Iceland in Nice through Wayne Rooney’s penalty. But goals from Ragnar Sigurdsson and Kolbeinn Sigthorsson turned the game in Iceland’s favour.
Gareth Southgate is the bookies’ favourite to replace him as England boss.