Alex Cifuentes, who says he was a close associate of Guzmán for years, told a New York City courtroom that he had told authorities of the bribe in 2016.
According to reporters in the Brooklyn courthouse, Mr Peña Nieto had requested $250m before settling on $100m.
Cifuentes claimed the delivery was made to Mexico City in October 2012 by a friend of El Chapo.
Cifuentes, a Colombian drug lord who has described himself as El Chapo’s “right-hand man”, worked as his secretary and spent two years hiding from authorities with him in the Mexican mountains, according to prosecutors.
President Peña Nieto and Mr Calderón immediately rejected the accusation, with the latter calling it “absolutely false and reckless”.