Noriega had been convicted in absentia in France of laundering money from cocaine profits in 1999, but France agreed to a new trial if he was extradited.
Despite finishing a long prison sentence in the US two years ago, Noriega remained in a Florida jail from where he was fighting extradition.
Panama also has an outstanding request for Noriega's extradition, after he was sentenced in absentia to 60 years in prison on charges of embezzlement, corruption and murdering opponents.
Juan Carlos Varela, Panama's foreign minister, said that Panama respects the US decision to extradite Noriega to France but will still try to get him back to Panama "to serve the sentences handed down by Panamanian courts".
Estelle Youssouffa, Al Jazeera's correspondent in Paris, said: "His [Noriega's] lawyers are hoping to get him out of jail as soon as in the next six months.
"But that doesn't mean that Manuel Noriega will be done with justice because Panama is hoping to have him extradited back home where he could face charges of torture and killing of political opponents."
French authorities had accused Noriega, who was ousted in a US invasion of Panama in 1989, of laundering about $7m in drug profits by purchasing luxury apartments with his wife in Paris.
They also said that he helped Colombia's Medellin drug cartel by authorising the transport of cocaine through Panama to the US.
Noriega, Panama's former intelligence chief, had been considered a valued CIA asset for years after he took power in 1982.
However, he was ousted as Panama's leader and put on trial for drug racketeering and related charges following a 1989 US military invasion ordered by George Bush Senior, the then president of the US.