Despite finishing his prison sentence two years ago, Noriega has since remained in a Florida jail where he has been fighting extradition.
Al Jazeera's Paul Werdel reports on Noriega's extradition to France
Hillary Clinton, the US secretary of state, signed the extradition order earlier on Monday, clearing the way for Noriega to be put on a plane to France.
His lawyers argued that he was a prisoner of war and should be sent back to Panama.
"If the rule of law is applied there should not be a trial in France," Yves Leberquier, one of Noriega's French lawyers, told France Info radio.
Frank Rubino, Noriega's principal lawyer in the US, told Al Jazeera he had only found out that the extradition was going ahead through the media.
"No one from the state or justice department here in the US has had the common courtesy to call us and tell us," he said.
Despite his conviction, Noriega can seek a new trial once he arrives in France.
Noriega had challenged his extradition to the US supreme court, but judges let stand a ruling by a federal appeals court that the US government can legally send Noriega to France without violating his rights as a prisoner of war under the Geneva Conventions.
The US government has supported France's extradition request and said the conventions do not apply to Noriega's case.
He was ousted from power in the 1989 US invasion of Panama and brought to trial in the US.
Three years later he was convicted of drug trafficking and money laundering charges, spending 20 years in jail.
Panama was once a major financial centre in Central America, and was used as a base to launder drug money through banks as well as a centre for the processing and transshipment of cocaine.
Multi-million dollar kickbacks went directly to Noriega during his tenure as head of the military from 1983 to 1990.