The 51-year-old guided England to their first major final in 55 years at Euro 2020 and his new deal, reported to have increased his salary to £5-6million, is performance related.
Southgate, whose previous deal was set to expire after the 2022 World Cup, said: “I’ve always wanted through my life to be fairly rewarded, but to deliver value for money for the organisation I worked for.
“That’s always been important to me and within the FA I’m very conscious of what we’ve been through as an organisation.”
The Football Association announced 124 redundancies and potential losses of up to £300m in June due to the impact of the coronavirus pandemic and Southgate agreed to a 30 per cent wage cut.
“I’m very conscious that we fund grassroots football and so, whatever we’ve earned over the period of time, I think we’ve been right to have to prove ourselves,” said Southgate, whose assistant Steve Holland has also signed a new two-year deal.
“I think now we have Wembley full more regularly and the prize money for reaching latter stages of tournaments, we want to make sure…that we’ve more than played our part in keeping the business side in the right place.
“That is a consequence of results and performances and bringing enjoyment to the country as well.
“In an ideal world you want a manager who cares about English football and about the organisation to be able to fulfil all those things.”
FA chief executive Mark Bullingham said: “I understand people will ask how we can afford this given the financial losses at the FA and, while I’m not going to go into details on the contract, I will say it’s a performance-related contract and any rises or increases and bonuses are self-funded by increases in either commercial revenue or tournament prize money.
“Both Gareth and Steve understand that and wanted it that way. They genuinely care about the organisation.
“We believe this is a really positive day for English football with the extension of a partnership that’s delivered so well for us as a country.
“We’re absolutely delighted that Gareth and Steve have chosen to continue and we look forward to the future together.”
Southgate has signed his deal after leading England to next winter’s World Cup in Qatar and is now committed to the role until after Euro 2024 in Germany.
He said: “I’d like to say how excited we are, the last five years have been an incredible experience.
“We can see what’s possible with the existing squad and some of the players coming through our age-group teams. We are grateful for the support of the FA.
“We felt it was important to qualify (before signing) so there was no question on focus. We are looking forward to the next few years to make some new memories.”
It is reward for the great strides England have made under Southgate, who later this month will celebrate five years in charge.
During that time the former England defender has led the Three Lions to a first World Cup semi-final since 1990, a third-placed finish in the Nations League and the final of the European Championship for the first time.
“We have to make sure the team constantly evolves,” he added. “We are now in a group of teams we believe can genuinely challenge. Six, seven years ago we went with hope, but now we can be genuinely positive. We know expectation is higher, but that’s good, the team is better than they were three years ago.
“When you’ve done work culturally and where they can challenge (for titles), you want to bring that to fruition. We’ve only won one World Cup, but we have to believe that’s possible, it’s an aim we have as a team.”
Should Southgate see out his new deal, he will have been national team manager for over eight years.
Asked how he would feel to serve a spell similar to greats like Sir Bobby Robson and Sir Alf Ramsey Southgate said: “I think that England has been a massive part of my life, supporter, player, under-21 manager and now manager and the people you’re talking about, I’ve always been aware of the history.”
Southgate has never ruled out a return to club management but, while his new deal arrives in the same month three Premier League managers have been sacked, he was not ready to consider leaving his current role.
“To step away when we think the next few years could have been exciting, that could be difficult to live with,” he said. “If this contract is the last, I will only be 53 at the end of it and I hope there’ll be a lot of my life at the end of it.”