Villepin, a potential candidate in next year's presidential election, denied the allegations, which claim to shed new light on the French political establishment's often shady relationship with former colonies in Africa.
Both Chirac and Villepin have said they will file defamation complaints against Robert Bourgi, who made the claims in France's Journal du Dimanche newspaper.
Bourgi, a lawyer with a network of African contacts who advised both men before changing camps in 2005 to aid now President Nicolas Sarkozy, said he "took part in handing over several briefcases to Jacques Chirac in person, at Paris city hall" when the future president was mayor in the 1980s and 1990s.
"There was never less than five million francs (€750,000). It could go up to 15 million," Bourgi said, giving a detailed account of how Chirac would offer him beer while allegedly putting away the bundles of cash.
"I remember the first handing over of funds in Villepin's presence. The money came from Marshal Mobutu (Sese Seko), president of Zaire (now Democratic Republic of Congo)."
"It was in 1995. He had given me 10 million francs that Jacques Foccart gave to Chirac," Bourgi said, referring to his predecessor who was president Charles de Gaulle's pointman for Africa and then briefly also for Chirac.
Chirac's lawyer, Jean Veil, said on Sunday he has been instructed by Chirac to file a defamation complaint against Bourgi over his claims.
Villepin told the France 2 television channel he would do the same.
"They are trying to stop me from running (for president), they have been putting spokes in the wheels for years, but I have thick skin," he said.
Bourgi claimed the money handed over amounted to "several million francs a year. More during elections".
"In the run-up to the 2002 presidential campaign (won by Chirac), Villepin asked me outright 'what steps to take'."
Bourgi said five African leaders came to Villepin's office: Senegal's Abdoulaye Wade, Burkina Faso's Blaise Compaore, Ivory Coast's Laurent Gbagbo and Congo-Brazzaville's Denis Sassou Nguesso and Gabon's Omar Bongo.
There, they handed over around $10 million for the 2002 campaign, he alleged.
Senegal "catagorically denies" the claims, a presidential office spokesman told AFP, while Gbagbo's former number two, Mamadou Koulibaly, confirmed that "there was a transfer of money" from Abidjan to Paris in 2002.
"Robert Bourgi is perfectly right," he told AFP, adding that the sum was "around two billion West African CFA francs (around €3m) brought from Abidjan to Paris in a suitcase."
"I told the president (Gbagbo) that we're a poor country and we shouldn't have to pay to finance elections for politicians in rich countries," Koulibaly lamented.
Bourgi said that since he started working for Sarkozy he had no longer brought in cases of African cash, although another former African advisor to Chirac, Michel de Bonnecorse, denied this.
The newspaper report led opposition Socialists to call for a judicial probe, Villepin allies to demand to know what Bourgi's current relationship is with Sarkozy and Bourgi himself to say he was available for judges to question.
Chirac, 78, was last week excused from attending his corruption trial over alleged ghost jobs created during his time at city hall. His doctors said he was afflicted by memory lapses.
Judges will this week also rule on Villepin's involvement in the Clearstream affair dating back to 2004 in which Villepin is accused of smearing his bitter rival Sarkozy.
Villepin, a suave diplomat best remembered for leading the charge against the Iraq war at the United Nations in 2003, was cleared of all charges in a first trial that ended last year.