Southgate will inform the English Football Association (FA) of his decision before Christmas, according to Sky Sports.
"We are delighted to confirm that Gareth Southgate is continuing as England Manager, and will lead our Euro 2024 campaign. Gareth and (assistant manager) Steve Holland have always had our full support, and our planning for the Euros starts now," FA CEO Mark Bullingham said in a statement.
England were knocked out of the World Cup in Qatar in a 2-1 loss to France in the quarter-final.
"Whenever I finish these tournaments, you need time to make the correct decision. Emotionally, you're going through many different feelings," Southgate told reporters when asked about his England future after their tournament exit.
Southgate, who led England to the 2018 World Cup semi-finals and the final of the delayed Euro 2020 tournament last year, signed a new contract through to the end of 2024 in November last year.
