Nardelli is the former CEO of Home Depot, the American DIY giant, and replaces Tom La Sorda who will remain as vice chairman and president.
Reports suggest Nardelli will not be paid a salary until Chrysler returns to profit.
Nardelli was part of the Cerburus team which studied the possibility of acquiring Chrsysler before it announced it wanted to buy majority stake in May.
Nardelli said: “I am confident that together we can continue the momentum of Chrysler’s recovery and return this great American icon to a path for global growth and competitiveness.”
Cerberus completed its takeover of Chrysler last week by paying £5 billion for an 80.1% stake in the company.
La Sorda said: "Nardelli has a proven track record of success and an unwavering focus on performance, and brings deep operational experience and a broad industry background to Chrysler. His background in operations will provide valuable knowledge as we continue Chrysler’s turnaround.”
In addition, Eric Ridenour, chief operating officer, has elected to leave the new company to 'pursue other opportunities'. The COO position will not be filled going forward.