The decision comes just two days after England suffered a second successive European Championship final defeat, losing 2-1 to Spain in Berlin on Sunday.
The 53-year-old's contract was set to expire later this year and he leaves having overseen four major tournaments and 102 games.
"As a proud Englishman, it has been the honour of my life to play for England and to manage England," Southgate said.
"It has meant everything to me, and I have given it my all.
"But it's time for change, and for a new chapter."
Formerly in charge of England's Under-21 side, Southgate took the reins of the senior team in September 2016 following Sam Allardyce's short-lived tenure.
He led England to the semi-finals of the 2018 World Cup and the Euro 2020 final - their first in 55 years - before losing the final on penalties to Italy at Wembley.
A quarter-final exit at the 2022 World Cup in Qatar followed before his last tournament in charge this summer at Euro 2024, where they fell short in the finale.
"I have had the privilege of leading a large group of players in 102 games. Every one of them has been proud to wear the three lions on their shirts, and they have been a credit to their country in so many ways.
"The squad we took to Germany is full of exciting young talent and they can win the trophy we all dream of. I am so proud of them, and 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.
"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."
FA chief executive Mark Bullingham paid tribute to Southgate for "making an impossible job possible" and said the process for appointing his successor is already underway.
"On behalf of English football, I would like to pay tribute to Gareth Southgate and to (assistant manager) Steve Holland for everything they have achieved," Bullingham said.
"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.
"Before Gareth, our longest time ranked in the top five in the world was seven months. In his tenure we have been ranked there for six years," he added.
"Gareth has made the impossible job possible and laid strong foundations for future success. He is held in the highest regard by the players, the backroom team, by everyone at the FA and across the world of football.
"We are very proud of everything Gareth and Steve achieved for England and will be forever grateful to them."
England's next match is on September 7th against the Republic of Ireland in the opening game of their Nations League campaign.
