The appointment would be effective from March 1, GM said in a statement.
Saxena replaces Lowell Paddock, who is moving to GM International Operations (GMIO) as Vice President, Planning & Programme Management.
GM Executive V-P and International Operations President Stefan Jacoby said: We are delighted to have Arvind join our team and lead us to a successful future in India. GM is committed to India under Arvind's leadership."
Saxena has an experience of about two decades in sales, marketing and management with several Indian and global automakers.
He began his career with Escorts in 1983, then moved to Bajaj Auto, followed by Maruti Udyog and Fiat.