The high court in the Himalayan state of Uttarakhand said this would help in the "preservation and conservation" of the highly polluted rivers.
It added that the "legal status" ensures that polluting the rivers would now amount to harming a human being.
Both rivers are considered sacred in India and are considered goddesses by the majority Hindu population.
The ruling comes a week after the Whanganui River in New Zealand became the first in the world to be granted the same legal rights as a person.
