“Didier for me is the best, there is no contest,” said Noel Le Graet at a press conference in Paris.
“Everyone on the executive committee of the FFF unanimously supports this extension.”
The deal will take the 49-year-old Deschamps through to the end of Euro 2020, meaning he will have been in charge for eight years.
The former midfielder, captain of the France side that won the 1998 World Cup and Euro 2000, was appointed in 2012 to succeed Laurent Blanc.
He took France to the quarter-finals of the 2014 World Cup and then to the final of Euro 2016 on home soil, where they lost in extra time to Portugal.
Les Bleus have also qualified for next year’s World Cup in Russia after topping their qualifying group.
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