Southgate had a contract until the 2024 European Championship, but admitted to feeling “conflicted” about staying on given what has often been a difficult 18 months.
But the former England defender will now remain in charge for a fourth major tournament.
In a statement on Sunday, the FA said: “We are delighted to confirm that Gareth Southgate is continuing as England manager, and will lead our Euro 2024 campaign.
“Gareth and Steve Holland have always had our full support, and our planning for the Euros starts now.”
Southgate led England to the World Cup semi-finals in Russia in 2018 and the final of last summer’s European Championship, before reaching the last eight in Qatar.
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In the build-up to this year’s tournament there had been significant criticism of Southgate following a run of poor results.
Relegation to League B of the Nations League after losing twice to Hungary, drawing two against Germany and a draw and defeat to Italy led to serious questions being asked about his future.
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But even after a positive response to the team’s World Cup run, Southgate stressed he needed a period of reflection to decide on the best course of action.
“I think, whenever I finish these tournaments, I’ve needed time to make correct decisions,” he said immediately after their exit.
“Emotionally you go through so many different feelings.
“The energy it takes through these tournaments is enormous.
“I want to make the right decision, whatever that is, for the team, for England, for the FA.
I’ve got to be sure whatever decision I make is the right one.”
Former England defender Gary Neville welcomed the news Southgate was staying.
“I think it’s the right decision,” he told Sky Sports News.
“When I saw early last week it was going to be discussed in the new year I didn’t think that would work, letting it hang for so long.
“The fact it has come out is welcome, it puts it to bed and allows everyone to focus on the next 18 months.
“It means a succession plan can be put in place.”
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Sky Sports News senior reporter Rob Dorsett: said: “The fact Southgate has decided, just eight days after England were knocked out by France, is significant.
“He’s recovered pretty quickly and there are a number of key factors which have convinced him it would be wrong to walk away now.
“Firstly, the players have all been hugely supportive of him. They were all adamant they wanted him to stay on.
“He also thinks England can win something. And that this squad, with the young players coming through, has a real chance of challenging in Germany in 18 months’ time for a European Championship. If he was to walk away now and someone else was to take that glory, I think he’d be pretty bitter about it and maybe regret it for the rest of his career.
“He spoke with his family about it and his assistant Steve Holland and he decided he needed to, he wanted to, and had the energy and desire to stay on as England’s boss until after Euro 2024.”
Southgate has won 49 of his 81 games as England manager, with 18 draws and 14 defeats, while England have scored 174 goals and conceded 57.
Only two previous managers have reached a half-century in the win column – World Cup winner Sir Alf Ramsey with 69 and England’s longest-serving manager Sir Walter Winterbottom on 78.