There have been as many as 41 injuries because drivers mistakenly believed they had put the automatic cars in “park”.
The recall covers cars and SUVs whose gearshifts could be confusing to drivers.
More than 850,000 vehicles in North America are affected, along with just over 250,000 elsewhere.
The affected models include 2012 to 2014 Dodge Charger and Chrysler 300 sedans and 2014/15 Jeep Grand Cherokee SUVs.
Fiat Chrysler said it would update the vehicles to automatically prevent them from moving, even if the driver fails to put the vehicle in park. The company did not say when the fix would become available to owners.
The US National Highway Traffic Safety Administration (NHTSA) said in February it had reports of 314 complaints, including 121 crashes after vehicles rolled away. Some hit buildings, drivers or other cars and many incidents occurred soon after the vehicles were bought.
Injury reports included three complaints of a fractured pelvis, and four others requiring some form of hospitalization.
An NHTSA spokesman said the agency would monitor the recall to ensure it took place as quickly as possible.
Fiat Chrysler said it began equipping the Charger and 300 with a new gearshift design for the 2015 model, while the Grand Cherokee was updated for the following year.
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