Southgate is the only manager, after 1966 World Cup winner Sir Alf Ramsey, to have led England men to the final of a major tournament.
He has coached England at four major tournaments, also reaching the World Cup semi-finals in 2018 and the quarter-finals in 2022.
In the major tournaments since 1966, before Southgate took charge in 2016, England have won seven knockout matches in total. Under Southgate, England have won nine of those matches, including two on penalties.
The pressure has increased on him this summer, with many fans feeling he is not getting enough out of a talented group of attacking players.
Some fans threw plastic cups at him after the 0-0 draw with Slovenia in the final group stage match of Euro 2024.
However, it allowed a large number of them to get back into the game thanks to their journey to the final.
“The team we have taken to Germany is full of promising young talent and they can win the trophy we all dream of,” Southgate added.
“We have the best fans in the world and their support has meant a lot to me. I’m an England fan and I always will be.
“I look forward to watching and celebrating the players as they continue to create even more special memories and connect and inspire the nation in the way we know they can.
“Thank you, England – for everything.”
The Prince of Wales, who is FA chairman, thanked Southgate for “creating a team that stands alongside the best in the world in 2024”.
“Thank you for demonstrating humility, compassion and true leadership under the most intense pressure and scrutiny,” he added.
“And thank you for being a class act in every way. You should be incredibly proud of what you’ve accomplished.”
