Frump replaces Tom von Bonsdorff who has moved to his home country Finland to pursue a new assignment within the Volvo Group after completing his tenure in India.
Volvo Auto India Director-Sales & Marketing Jyoti Malhotra was the acting Managing Director in the interim.
He added: "My role here is to continue and accelerate the robust growth for Volvo cars in India. I am well aware of the diversity and challenges India poses and I believe my experience in other emerging markets will help significantly in achieving our goals here."
Frump has been associated with Volvo Car Group for over eight years. His previous stint with the group was in Sweden where he worked as a senior director within the marketing function.