Ngaissona, who is from the Central African Republic and sits on the board of the Confederation of African Football (CAF), has been in a jail near Paris since his arrest on December 12.
The one-time sports minister, who is head of the Central African Republic's football association, was controversially elected to the executive board of the CAF general assembly in February.
The International Criminal Court (ICC) issued a warrant in December for Ngaissona for allegedly coordinating so-called anti-Balaka militias which emerged after civil war broke out in the Central African Republic in 2013.
The militias, set up to defend Christian communities from mostly Muslim rebels, are accused of a host of human rights abuses including mass killings and mutilations.
The arrest came just weeks after another suspected militia leader -- Alfred Yekatom, known as Rambo -- was detained in the Central African Republic (CAR) and transferred to The Hague.
The decision to extradite Ngaissona was made by magistrates at the court of appeal in Paris.
"I was a spokesman who brought peace to the Central African Republic and not a warlord," Ngaissona told the court during a hearing on December 19.
France, the former colonial power, sent 2,000 troops to help stabilise the conflict-torn CAR in 2013 and attempted to detain Ngaissona a year later during an operation in his fiefdom in the north of the capital Bangui.
The ICC considers Ngaissona the "most senior leader and the 'National General Coordinator' of the anti-Balaka" and therefore responsible for crimes in several parts of the country.
The alleged crimes include murder, torture, mutilation, intentionally targeting and displacing civilians, pillaging and enlisting child soldiers.
In 2015, Ngaissona was barred from running in presidential elections over concerns about his role in the violence, but has previously said that "everything I've done has been for the good of my country".
In February, he was elected to the CAF board seat representing eight central African nations. The CAF said his candidacy respected "strict statutory criteria" but noted the body did not have an ethics committee.
"If the allegations were true, I wouldn't be here today," Ngaissona told AFP in February, saying he didn't want "to mix politics and sport".
The ICC has launched investigations into at least eight African countries since its establishment in 2002, including several into the violence in CAR.
Jean-Pierre Bemba, former vice president of the Democratic Republic of Congo, was convicted in June 2016 for war crimes committed by his rebel army in CAR in 2002-2003, but this was overturned on appeal two years later.
A second probe was opened in September 2014 into atrocities committed by armed militias during the most recent civil war.