THULASENDRAPURAM, India - Waking up to the news of U.S. Sen. Kamala Harris’ election as vice president, overjoyed people in her Indian grandfather’s hometown set off firecrackers and offered prayers last Sunday. Groups gathered at street corners in Thulasendrapuram, a tiny village of 350 people, reading newspapers and chatting about Joe Biden and Sen. Harris’ victory before moving to a temple.

A woman wrote in color powder outside her home: “Congratulations Kamala Harris. Pride of our village. Vanakkam (Greetings) America.”

Most of them had gone to sleep by the time Mr. Biden clinched the winning threshold of 270 Electoral College votes, making Sen. Harris the first woman and the first person of African-American and South Asian descent to be elected vice president.

“For two or three days we kept our fingers crossed while the result was delayed,” said village resident Kalidas Vamdayar. “Now it’s a joyful moment for us. We are enjoying it.”

“We will celebrate with firecrackers, distributing Indian sweets to people and praying in the temple,” Mr. Vamdayar said. “We will request her to come here. She would have heard our voice and she may come.”

Tamil Nadu state Food Minister R. Kamraj led about 100 people at the Dharma Sastha temple for a 20-minute prayer during which the idol of Hindu deity Ayyanar, a form of Lord Shiva, was washed with milk and decked with flowers by the priest. He chanted hymns after lighting oil lamps, and the villagers bowed their heads in respect.

“Kamala Harris is the daughter of our village,” said Aulmozhi Sudhakar, a village councilor. “From children to senior citizens, each one of us is awaiting the day she will take the oath as the vice president of the U.S.”

There was more singing, dancing and firecrackers throughout the day in the village, where cutouts and posters wishing Sen. Harris a “grand success” adorned walls.

People congregated in groups of 30 to 40 exchanging sweets, delicacies and snacks at different spots. They seemed to be celebrating Diwali, the most popular Hindu festival of lights, a week ahead of time.

Young children carrying placards with photos of Sen. Harris ran around the village. Several politicians from nearby districts visited the village with their supporters, meeting local residents and visiting the temple. Musicians played wind and string instruments with cymbals and drums.

J. Sudhakar, who organized prayers on Election Day, expressed his wish that Sen. Harris will visit. As Americans voted, around 50 residents, with folded hands, lined up in the temple that reverberated with the sound of ringing bells, and a Hindu priest gave them sweets and flowers as a religious offering.

Women in the village, which is located 215 miles from the southern coastal city of Chennai, used bright colors to write “We Wish Kamala Harris Wins” on the ground, alongside a thumbs-up sign.

The lush green village is the hometown of Sen. Harris’ maternal grandfather, who moved to Chennai, the capital of Tamil Nadu state, decades ago.

Inside the temple where people have been holding special prayers, Sen. Harris’ name is sculpted into a stone that lists public donations made to the temple in 2014, along with that of her grandfather who gave money decades ago.

Sen. Harris’ late mother also was born in India, then moved to the United States at the age of 19 to study at the University of California. She married a Jamaican man, and they named their daughter Kamala, Sanskrit for “lotus flower.”

Indian Prime Minister Narendra Modi described Sen. Harris’ success as path-breaking, and a matter of immense pride, not just for her relatives but also for all Indian-Americans.

“I am confident that the vibrant India-U.S. ties will get even stronger with your support and leadership,” the prime minister tweeted.

There has been both excitement—and some concern—over Mr. Biden’s choice of Sen. Harris as his running mate. Prime Minister Modi had invested in President Trump, who visited India in February. Mr. Modi’s many Hindu nationalist supporters also were upset with Sen. Harris when she expressed concern about the divided Himalayan region of Kashmir, whose statehood India’s government revoked in August last year.

Sen. Harris stood by Pramila Jayapal, another U.S. congresswoman of Indian origin, when Indian External Affairs Minister S. Jaishankar refused to attend a meeting in the United States over her participation last year. Rep. Jayapal had earlier moved a resolution on the Kashmir issue critical of India in the U.S. House of Representatives.

Rights groups accuse India of human rights violations in Indian-controlled Kashmir, where insurgent groups have been fighting for independence or merger with neighboring Pakistan since 1989.