Known as a powerful advocate for contemporary and traditional artists in India, hers is the first international appointment to the museum board.
Ambani, a former actor, is married to industrialist Anil Ambani.
PEM is the oldest continually-operating museum in the US and the second-largest in New England.
Image: Tina Ambani, founder and patron of Harmony Art Foundation, at Christie's auction house in London. | Photograph: Adrian Dennis/AFP/Getty Images