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Southgate’s salary is thought to have increased from £3million per year to around £5m plus bonuses, taking him close to the £6m earned by predecessor Fabio Capello.
The 51-year-old has been in talks with FA chief executive Mark Bullingham and technical director John McDermott, and the deal comes after England secured qualification for next year’s Qatar World Cup with wins over Albania and San Marino last week.
Southgate’s assistant Steve Holland has also agreed a new deal until 2024.
Southgate, who is due to address the media over Zoom on Monday afternoon, said in a statement: "I am delighted that Steve and I have been able to extend our stay in our respective roles. It remains an incredible privilege to lead this team.
“I would like to take this opportunity to thank Mark, John and the Board for their support - and of course the players and support team for their hard work. We have a great opportunity in front of us and I know they and the fans are all excited about what this squad could achieve in future."
Under Southgate and Holland, England reached the semi-final of the 2018 World Cup and lost on penalties to Italy in the final of Euro 2020 at Wembley in July.