This was Elliott's second stint as boss of its UK operation, having previously headed up the company from 1999.
He was in charge as Chrysler merged with Mercedes-Benz.
Elliott had also headed the firm's Chinese business, and returned to the UK in January after last October's departure of Peter Lambert.
In March Elliott criticised the model mix he inherited, and said this needed to be slimmed down.
Since then Chrysler has moved to push the Dodge brand and dropped models like the Crossfire and PT Cruiser.
No reason was given for Elliott's exit.