The Three Lions lost 2-1 in Berlin on Sunday, their second consecutive Euros final defeat, having been beaten on penalties by Italy at Wembley three years ago.
The 53-year-old managed his country for 102 games in eight years in charge.
His contract was set to expire later this year.
“As a proud Englishman, it has been the honour of my life to play for England and to manage England,” said Southgate.
“It has meant everything to me, and I have given it my all.
“But it’s time for change, and for a new chapter.”
Football Association chief executive Mark Bullingham said the process to appoint Southgate’s successor has started and “we aim to have our new manager confirmed as soon as possible”.
He added the FA “have an interim solution in place if it is needed” and will not comment further on the process until a new boss is appointed.
England’s next match is against the Republic of Ireland in the Nations League on 7 September.
Southgate is the only manager bar 1966 World Cup winner Sir Alf Ramsey to lead the England men’s team into a major tournament final.
He managed England at four major tournaments, also reaching the World Cup semi-finals in 2018 and quarter-finals in 2022.
In 25 tournaments since 1966 before Southgate took over in 2016, England won seven knockout games in total.
Under Southgate, England won nine such matches.
Pressure mounted on him this summer, with many fans believing he was not getting enough out of a talented group of attacking players.
Some supporters threw plastic cups at him after the 0-0 draw with Slovenia, in the final match of the group stage at Euro 2024.
However, he got many of them back onside with their run to the final.
“The squad we took to Germany is full of exciting young talent and they can win the trophy we all dream of,” added Southgate.
“We have the best fans in the world, and their support has meant the world to me.
I’m an England fan and I always will be.
“I look forward to watching and celebrating as the players go on to create more special memories and to connect and inspire the nation as we know they can.
“Thank you, England – for everything.”
The Prince of Wales, who is president of the FA, thanked Southgate for “creating a team that stands shoulder to shoulder with the world’s finest in 2024”.
“Thank you for showing humility, compassion, and true leadership under the most intense pressure and scrutiny,” he added.
“And thank you for being an all-round class act.
You should be incredibly proud of what you’ve achieved.”
Southgate, who replaced Sam Allardyce after his short-lived spell, won 61 of his 102 games in charge of England, drawing 24 and losing 17.
The former defender, who won 57 caps for England between 1995 and 2004, has been involved in the England set-up since 2013, having managed the under-21s for three years prior to taking the top job.
His only experience in club management was at Middlesbrough from 2006 to 2009.
Southgate thanked his players and backroom staff, calling assistant Steve Holland “one of the most talented coaches of his generation”.
“I joined the FA in 2011, determined to improve English football,” he added.
“I hope we get behind the players and the team at St George’s Park and the FA who strive every day to improve English football, and understand the power football has to drive positive change.”
Bullingham said Southgate had made “the impossible job possible and laid strong foundations for future success”.
“We are very proud of everything Gareth and Steve achieved for England, and will be forever grateful to them,” added Bullingham.
“Over the last eight years they have transformed the England men’s team, delivering unforgettable memories for everyone who loves the Three Lions.
“We look back at Gareth’s tenure with huge pride – his contribution to the English game, including a significant role in player development, and in culture transformation has been unique.”
