A Togolese government source says the 69-year old will face court in Lome for questioning on Monday.
The investigation involves a complaint from an Emirati businessman, Abbas Al Yousef, who alleges he was the victim of a 37 million euro fraud.
Al Yousef claims Le Floch-Prigent was acting as his personal advisor during the alleged fraud.
The case involves a complex set of circumstances, with accusations that a network claimed to have access to 209 million euros in a Togolese account left by former Ivorian military ruler Robert Guei, who was killed in 2002.
Al Yousef alleges the 37 million euros was embezzled from him in the affair.
Togo's former minister of territorial administration, Pascal Bodjona, and another Togolese businessman have both been charged over the allegations.
Le Floch-Prigent lawyer, Patrick Klugman, has denounced the extradition, saying his client appeared to be the victim of internal politics in Togo.
"[This is] an abduction and in no way an extradition, because my client was arrested and handed over to the Togolese authorities without the intervention of any judicial authority," he said.
Klugman later said his client had not been abducted, but stressed the “forms of extradition as we know them were not respected.”
He added he knew where Le Floch-Prigent was being held and that his client had been able to consult with a lawyer in Togo. But he also said he feared for Le Floch-Prigent's health.
Le Floch-Prigent, currently an oil industry consultant, has already served jail terms in France for corruption dating from his time as head of Elf from 1989 to 1993.
He was first jailed for five months in France in 1996 for misusing company assets.
The oil giant Total tover Elf in 2000.
Le Floch-Prigent was jailed again in 2003 on other charges and freed on probation in 2004 on health grounds, on condition that he pay compensation, at a rate based on
his own revenues, to Total for the case involving Elf.
He was sent back to jail for six months in 2010 for failing to pay adequate compensation to Total.