The 43-year-old, who captained France to the 1998 FIFA World Cup and EURO 2000 trophies, replaces fellow FIFA World Cup and Euro-winning team-mate Laurent Blanc, who turned down a new two-year contract last weekend.
Blanc had guided the French to the UEFA EURO 2012 quarter-finals, the minimum requirement of the FFF, but dressing room discord and two outbursts by Samir Nasri had not helped Blanc's cause.
Deschamps immediately became the favourite and lent credence to the fact by quitting Marseille last Monday. "Noel Le Graet, President of the FFF, and Didier Deschamps reached agreement after the conclusion of their talks for him to be named France coach," read the statement.
Both men are to hold a joint press conference on Monday at the federation headquarters at 1530 GMT.
Deschamps' contract is expected to be for two years, taking him up to the 2014 FIFA World Cup finals in Brazil, and will be assisted by his faithful Marseille lieutenant Guy Stephan.
Deschamps' first task will be to prepare the squad for a high profile friendly against Copa America champions and FIFA World Cup semi-finalists Uruguay in Le Havre on 15 August, while their first Brazil 2014 qualifier will be against Finland on 7 September.
However, with just one automatic qualifying spot up for grabs in the shape of group winners, France face a tough task as two-time European champions and FIFA World Cup holders Spain are in their same group. Belarus and Georgia are the other two sides.