Chelsea, MICHIGAN (Reuters) - Fiat Chrysler Automobiles NV <FCHA.MI> <FCAU.N> chief of Jeep brand Mike Manley said Thursday software fixes for 1.1 million vehicles that were recalled for rollaway risks, including the Jeep Grand Cherokee, will be available by the end of this month.

A Grand Cherokee was recently involved in the death of actor Anton Yelchin. Manley said the company was conducting a "thorough investigation" of the incident but did not estimate when such a probe would be completed.

Manley spoke with reporters at a driving event for new FCA vehicles in Chelsea, Michigan.

(Reporting by Bernie Woodall; Editing by Bernadette Baum)