The story of Geeta, a Hindu woman in her early 20s, has captivated people in both countries at a time of heightened tension and border clashes between the nuclear-armed rivals.
"It doesn't matter if we find her parents or not, she is a daughter of India and we will take care of her," Indian Foreign Minister Sushma Swaraj told a news conference.
Geeta was about 11 when she crossed from India into Pakistan. Exactly how is not clear but Geeta mimes an explosion and shows how she ducked and ran before being caught by armed men.
At first, she was kept at a children's home in Lahore, where she was given the Muslim name Fatima.
She would point at maps of India, especially to an area in the south of Jharkhand until she was able to finally communicate she was from India, not Pakistan.
Early on Monday, Geeta left the charity bound for the airport in the city of Karachi for a flight to New Delhi.
Wearing a traditional red outfit with her head covered by a loose scarf, she smiled and waved to television cameras after leaving the airport in New Delhi.
"Geeta stayed with us for 13 years. Now it's time for her to go home," said Faisal Edhi, son of the founder of Edhi Foundation, a Pakistani charity that looked after the girl.
She headed to meet a family from Bihar whom she says she recognised from photos sent by the Indian High Commission in Pakistan.
Swaraj said if a DNA test proves the family is not hers she will be sent to a temporary home run by a charity and the search for her parents would continue.
Hostilities have kept apart many families since majority-Hindu India and Muslim Pakistan became separate countries in 1947.
Geeta's arrival came after Indian and Pakistani forces exchanged fire along a 100 km (60 mile) stretch of their frontier overnight, an Indian Border Security Force spokesman said.
Her story attracted much attention following the release this year of a film called "Bajrangi Bhaijaan", in which an Indian man finds a mute Pakistani girl and tries to reunite her with her family.
The scriptwriters were unaware of Geeta's story but the movie led to a surge in interest.
