US Secretary of State Hillary Clinton signed a "surrender warrant" after all judicial challenges were resolved.
French officials later confirmed he was on board an Air France flight to Paris.
A court in France convicted Noriega in his absence in 1999 for laundering money through French banks, though it says he will be granted a new trial.
The 76-year-old had wanted to be sent back to Panama after finishing his 17-year jail sentence in 2007.
But in February the US Supreme Court rejected his final appeal against extradition to France.
Panama's government said it respected the "sovereign decision" the state department took to extradite Noriega.
But it insisted it would seek his return to serve outstanding prison sentences there.
Noriega was escorted onto an Air France passenger jet at Miami International Airport on Monday afternoon, shortly after Mrs Clinton signed the extradition order, US officials said.
French prison officials took custody of him once he was on board, sources in Paris told the AFP news agency.
A spokesman for the French justice ministry, Guillaume Didier, said that when Noriega arrived in Paris on Tuesday morning, he would go before prosecutors to be notified of the arrest warrant against him.
A judge would then decide whether to place him under temporary detention until his case was referred to a criminal court, he added.
Mr Didier said France had been notified of the extradition two weeks ago.
But Noriega's lawyer in Miami, Frank Rubino, told the BBC he had not been notified and had only learned of his client's transfer from the media.
"Usually the government has - does things in a more professional manner and respects common courtesy and we're shocked that they didn't," he said.
"I'm surprised that they didn't put a black hood over his head and drag him out in the middle of the night," he added.
'Prisoner of war'
Noriega was Panama's military intelligence chief for several years before becoming commander of the powerful National Guard in 1982 and then de facto ruler of the country.
He had been recruited by the CIA in the late 1960s and was supported by the US until 1987.
But in 1988 his indictment in the US on charges of drug trafficking left frayed relations.
After a disputed parliamentary election the following year, Noriega declared a "state of war".
A tense stand-off followed between US forces stationed in the Panama Canal zone and Panamanian troops.
By mid-December, the situation had worsened so much that President George H W Bush launched an invasion - ostensibly because a US marine had been killed in Panama City, although the operation had long been planned.
Noriega initially took refuge in the Vatican embassy, where US troops bombarded him for days with deafening pop and heavy metal music.
He eventually surrendered on 3 January 1990 and was taken to Miami for trial.
In 1992, he was convicted of drug trafficking, money laundering and racketeering.
He was handed down a 40-year prison sentence, later reduced to 30 years, and then 17 years for good behaviour.
Noriega was convicted in absentia in France in 1999 for allegedly using $3m (£1.9m) in proceeds from the drug trade to buy luxury apartments in Paris, and sentenced to 10 years in prison.
Shortly before the completion of his US jail sentence, the French government sought Noriega's extradition.
When his lawyers attempted to fight the request, he was forced to remain in US custody in Miami.
His legal team argued that he should not have been extradited to a third country such as Franc.
They said that as a prisoner of war of the US, the Geneva Conventions required Noriega to be returned to Panama.
But the US Supreme Court upheld a federal appeals court ruling that the US government could send him to France without violating his rights as a prisoner of war.
