"Noel Le Graet, president of the French Football Federation, and Didier Deschamps have finished their discussions and have reached an agreement for the nomination of Mr Deschamps as France coach," an FFF statement read.
A news conference will take place at on Monday at the feederation's headquarters.
France's 1998 World-Cup winning captain left Olympique Marseille almost a week ago and replaces Laurent Blanc, who quit following the national side's Euro 2012 quarter-final exit.
Deschamps' first job will be to unite an often fractious squad as they bid to qualify for the 2014 World Cup in Brazil via a difficult group including world champions Spain.
The federation has summoned four players, including midfielder Samir Nasri who launched a foul mouthed rant at a reporter, to a disciplinary hearing over "misbehaviour" at Euro 2012 - underlying Deschamps' problems.
Blanc, who took over in 2010 after a dreadful World Cup where the players mutinied, left after his side produced a soulless performance in the 2-0 defeat by eventual winners Spain at the European championship in Ukraine and Poland.
Blanc took time to decide if he would sign a new contract and then opted to walk away, with media reports saying some of Europe's top clubs would seek his signature.
Deschamps, who managerial record is patchy, also needed several days to make up his mind to accept the job.
He led modest Monaco to the Champions League final in 2004 and took Juventus back into Serie A in 2007 following their match-fixing demotion only to resign straight afterwards having clashed with the board over signings.