Ranieri's appointment was held up by French league (LFP) rules that prohibit the appointment of any manager above the age of 65. The Italian turned 65 in October.
"The Legal Committee of the LFP, which met on Tuesday 13 June 2017, decided to authorise the signing of a professional coaching contract between Mr Claudio Ranieri and FC Nantes," the league's governing body said in a statement on Tuesday.
Leicester's maiden English top-flight title under Ranieri's leadership was hailed as one of sport's most remarkable achievements after the team began the season as 5,000-1 outsiders.
But the Italian was sacked nine months after lifting the trophy, with Leicester hovering above the relegation zone following indifferent results.
Ranieri has also coached French club Monaco, Italian sides Napoli, Fiorentina, Juventus, AS Roma and Inter Milan, England's Chelsea and Spanish teams Valencia and Atletico Madrid.
Nantes finished seventh in Ligue 1 last season and coach Sergio Conceicao left the club this month to take charge of Portuguese side Porto.
(Reporting by Simon Jennings in Bengaluru, editing by Ed Osmond)
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