Wagh, who will take charge with immediate effect, has also been appointed as a member of the Executive Committee (ExCom), the company said in a statement.
He is currently head of the company's heavy and medium commercial vehicles division.
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Wagh will closely work with Ravindra Pisharody for a smooth transition, it added.
Citing personal reasons, Pisharody had resigned on June 5, the day the company announced the appointment of Executive Director Satish Borwankar to a newly created position of Chief Operating Officer.
The company had also extended the tenure of Borwankar as executive director by two years.
Tata Motors said the replacement of Wagh as the 'Head of Product Line MHCV' will be announced in due course.
In the meantime he will continue to oversee the MHCV related scope of responsibilities, it added.