Naudin, a criminologist and aviation security expert who was arrested in Cairo on February 4, is wanted in the Caribbean nation on suspicion of helping pilots Pascal Fauret and Bruno Odos flee to France in October after they had been sentenced to 20 years in prison for drug trafficking.
The pair, who maintain their innocence, were arrested in March 2013 as they were about to depart from Punta Cana in a private jet found to be carrying 680 kilos (1,500 pounds) of cocaine.
They somehow managed to flee and return to France -- an escape that Dominican prosecutors allege Naudin facilitated.
Prosecutor Francisco Dominguez said Naudin would be charged with conspiracy and the trafficking of migrants after reaching Santo Domingo, where he was expected to arrive around midnight after a stopover in New York.
Naudin will make an initial court appearance within 48 hours of arrival, the prosecutor told journalists.
Fauret and Odos fled back to France vowing to clear their names, but were rearrested in November near the French city of Lyon.
Paris has ruled out extraditing them.
But France's foreign ministry on Thursday confirmed Naudin had been extradited.
"France has done everything it could to support Naudin," a statement said. "Our embassy in Santo Domingo is following the situation closely and is ready to provide consular assistance."
Naudin's wife Michele said he would not receive a fair trial in Santo Domingo.
"The Dominican Republic has already said he will be convicted. We know that there is no justice there, and France knows this, yet it let him leave" Egypt, she told AFP.
Olivier Cadic, France's senator representing overseas nationals, called Naudin's extradition "very bad news for our country."
"There is real concern at how France has managed this affair," he told AFP.