Deschamps replaces Laurent Blanc, who stepped down from the helm of Les Bleus last week following the fallout of their Euro 2012 quarter-final exit to eventual winners Spain.
A statement on www.fff.fr last night read: “Noel Le Graet, FFF president, and Didier Deschamps have finished their talks and have reached an agreement for the appointment of Mr Deschamps as coach of the France team.”
Deschamps, who captained France to their 1998 World Cup and Euro 2000 triumphs, was quickly installed as favourite to succeed Blanc after he left his post at Marseille by mutual consent last week.
The 43-year-old guided OM to one Ligue 1 title and a record three successive League Cups in as many years on the south coast.
Deschamps, who has also previously managed Juventus and Monaco, endured a difficult campaign last season, however, as OM managed only 10th place in Ligue 1.
As a player, Deschamps represented Nantes, Marseille, Juve, Chelsea and Valencia before hanging up his boots in 2001. He also won 103 caps for France, 52 of which were as captain.
During his playing career he won a host of titles, including five league crowns in France and Italy, two Champions Leagues and two domestic cups.
Deschamps’ first game in charge is set to be against Uruguay in Le Havre on August 15.
He could be without a number of his star names before then, however, as the FFF continue to sift through the fallout of a Euro 2012 campaign that was undermined by off-field problems.
Last week the governing body opened disciplinary proceedings against Samir Nasri, Hatem Ben Arfa, Jeremy Menez and Yann M’Vila, who are set to be called in front of a disciplinary committee.
Manchester City midfielder Nasri fell foul of the FFF following his heated argument with a journalist in the wake of Les Bleus’ last-eight loss to Spain, while Newcastle forward Ben Arfa was allegedly embroiled in a dressing-room altercation following the 2-0 defeat by Sweden in France’s final Group D outing.
Paris St Germain midfielder Menez is to be investigated after allegedly gesturing at keeper Hugo Lloris, while Rennes midfielder M’Vila upset the FFF when he ignored Blanc following his substitution against Spain.
The unsavoury claims have brought back memories of France’s disastrous 2010 World Cup, when Les Bleus crashed out at the group stage after the players refused to train following the expulsion of Nicolas Anelka.
On that occasion, Anelka, Patrice Evra, Franck Ribery and Jeremy Toulalan were hit with bans of varying lengths by the FFF.
France begin their qualifying campaign for the 2014 World Cup with an away match against Finland on September 9 before they host Belarus four days later.
Also in Group I are defending champions Spain and Georgia.