Winterkorn faces four counts, including conspiracy to defraud the US and wire fraud.
American prosecutors say Winterkorn knew of the company's emissions cheating as early as May 2014 but decided to continue with the fraud, the Justice Department said in a statement.
While Winterkorn cannot leave Germany due to the threat of an arrest on an international warrant, Diess has managed to obtain assurances that he is free to travel to the US and elsewhere, German media reported.
US authorities have also reportedly agreed to inform Diess in advance if he were to be charged or if any arrest warrants against him were issued.
VW did not immediately respond to AFP's request for a comment. Diess is the second CEO to be named at Volkswagen after longtime boss Winterkorn quit days following the group's startling admission that it installed software in 11 million diesel vehicles worldwide designed to cheat regulatory emissions tests.
A former BMW executive, Diess has been seen as relatively untainted by the crisis as he joined VW only two months before the emissions cheating scandal broke in September 2015.
Winterkorn has not only US investigators hot on his heels, but also faces the possibility of losing his fortune as Volkswagen is examining whether to make him liable for the billion-dollar losses incurred as a result of dieselgate, German media reported.
According to the Frankfurter Allgemeine Zeitung, Winterkorn made more than 100 million euros ($120 million) over 10 years at Volkswagen. His pensions are worth almost 30 million euros.
Dieselgate has so far cost VW more than 25 billion euros ($31 billion) in buybacks, fines and compensation, and the carmaker remains mired in legal woes at home and abroad.