Southgate's new deal - worth just over 3 million euros a year - will last until after the 2022 World Cup in Qatar.
"I am delighted to have the opportunity to lead the national team through the next two major tournaments," said the former England interntional.
"The job remains an incredible privilege and a true honour. Experiencing at first hand how the nation united behind the team this summer was something special and it will be great to see how far this young squad can go in the years to come."
England, who lost to Croatia in the semi-final, went down to Belgium in the third place play-off. France crushed Croatia in the final 4-1.
"I must acknowledge the hard work and commitment of my staff and the players over the last two years," added Southgate. "I have learned a great deal from them and their passion and professionalism in representing England has been an inspiration to my own work."
Southgate replaced Sam Allardyce in September 2016. He left within two months of taking up the post after undercover newspaper reporters recorded him making inappropriate remarks about the former England manager Roy Hodgson.
Martin Glenn, the FA's chief executive, said Southgate had restored genuine optimism in England's ability to be a viable contender for trophies.
"Securing Gareth on a longer term contract was always a priority for us," said Glenn. "He has performed remarkably well and has given everyone the belief that England can compete on a world stage again."