The match in Doha will be at the 50,000-seater Khalifa International Stadium.
It will take place six days after Chelsea play Manchester United in the Premier League, with Liverpool playing Birmingham City five days before the England match.
England sealed their qualification for the World Cup in South Africa with two games to spare when they beat Croatia 5-1 on 9 September. It means they can afford to start thinking early about plans for next summer's tournament.
They still have two qualifiers to play, away to Ukraine and at home to Belarus next month, before the game against Brazil.
Three more friendlies are planned for next year, one of which is likely to be against Japan in Austria, where England plan to have a pre-tournament training camp at altitude.
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