The importance of Indian culture is also highlighted.
Ms Chopra took the crown at a glittering ceremony in London's Millennium Dome on Thursday.
The bookmakers' favourite, she beat 94 other contestants to claim the title - and $100,000 (£70,000) in prize money.
It was India's second successive win, and the fourth in seven years.
The country now holds both the Miss World and Miss Universe titles.
Miss Chopra's grandmother Madhu Jyotsna, speaking from the family home in the state of Uttar Pradesh, said she was "proud and excited".
Miss Chopra has said she wants to become a clinical psychologist.
However, the title means she is likely to become an instant celebrity in India, where the contest is extremely popular.
Successful contestants have used it as a springboard to fame, with previous winners going on to become top Bollywood stars.
Culture
The BBC's Jill McGivering in Delhi says the activities and public appearances of previous winners are closely followed by the Indian media.
The importance of Indian culture is also highlighted.
One newspaper quoted Priyanka Chopra as saying she was beautiful because she was Indian.
Sathya Saran, editor of the women's magazine Femina which organises the Miss India contest, said winning the Miss World and Miss Universe titles had a positive impact on the position of Indian women.
"Events like this do a lot to raise the traditionally low self-esteem of our women," she says.
Cosmetics market
However, some Indian women's groups criticise beauty pageants as demeaning and undermining women's status in society.
Some critics also argue that the reason why Indian women may be winning so many competitions is because international cosmetics companies are eager to penetrate the Indian market.
The beauty business, modelling and fashion have boomed in recent years with special courses aimed at young, mostly middle class women.
There have also been concerns that the celebration of thin women is one reason for the apparent increase in cases of anorexia nervosa amongst teenage girls in India.