The Italian giant changed its name after completing the purchase of Chrysler in January, nearly five years after Marchionne took the helm of the US automaker as it emerged from a government-backed bankruptcy restructuring.
The company said its shares would be listed in New York and Milan, and that Fiat shareholders would receive one Fiat Chrysler common share for each Fiat share they hold. Fiat Chrysler will be resident in the UK for tax purposes.
"October 1. That's the target," Marchionne told reporters during a tour of a Chrysler plant in suburban Detroit, Michigan.
"But it's a target. It could slip thirty, sixty or ninety days," he said, noting the company has to prepare an extensive set of documents before it can actually list its shares on the NYSE.
Marchionne also said he does not believe the crisis in the Ukraine will have any spillover effects on the European economy or Fiat Chrysler's investment in Russia, where it is preparing to build Jeeps with a Russian partner.
"It's an unfortunate set of circumstances," Marchionne said. "It should be resolved diplomatically."