The 68-year-old - who will need special permission to take up the post because he is over 65 - replaces Christian Gourcouff who was sacked three weeks ago.
He will be the 15th coach since Waldemar Kita became president of the club in 2007.
Domenech, who last led a French top flight team between 1988 and 1993, took France to the final of the 2006 World Cup in Germany.
He was in charge of the squad for the 2010 World Cup in South Africa. The campaign descended into farce after players refused to attend a training session.
Since leaving the France job, Domenech has been a football pundit on French television.
He attended Nantes’ 3-0 defeat at Lyon on Wednesday night’s which allowed the hosts to go top of Ligue 1 on goal difference ahead of Lille.
Paris Saint-Germain, who dismissed their coach Thomas Tuchel on Wednesday night after their 4-0 win over Strasbourg, are third, one point behind.
