The severe cyclone, packing winds of around 120 kilometres per hour, barrelled in from the Bay of Bengal to make landfall near Pulicat, some 50 kilometres north of state capital, Chennai.
Vardah, which means Rose in Arabic, inundated large areas and uprooted thousands of trees and power lines as millions remained indoors to escape the fury of the cyclone.
Ten people died in the storm, most of them in incidents of collapsing homes and trees, state disaster management chief K Satyagopal said.
The region saw widespread rainfall, with schools, markets and offices closed in Chennai and other coastal areas. Four deaths were reported from Chennai, one of India’s largest cities, which officials said was “worst-affected” by flooding.
The cyclone comes around a year after two waves of floods swamped the city, killing more than 300 people.
Teams from the army and national disaster management authority were carrying out relief and rescue operations overnight, Satyagopal said.
Indian Meteorological Department official P Mohapatra told reporters that the “worst was over” as the cyclone travelled about 300 kilometres inland, adding that it would lose its intensity by late Monday.
Trains were suspended in the region and more than 50 flights were cancelled, diverted or delayed at Chennai airport, broadcaster NDTV reported.
The government had also taken precautions for the safety of the Kalpakkam nuclear power plant in the region, officials said.
An estimated 17,500 people living in low-lying coastal areas were evacuated in Tamil Nadu and the neighbouring state of Andhra Pradesh. Of these, 10,500 people were sheltered in about 100 relief camps.
“We have gone without food today and there is no place to stay tonight,” a villager who lost her hut in Pulicat told broadcaster NDTV. “It is raining incessantly. We are helpless as we have to spend the night outdoors in darkness”.
State disaster officials said the death toll could rise further and the damage could be accurately estimated by Tuesday.
According to US space agency NASA, cyclone Vardah evolved out of the same tropical storm that caused widespread flooding in Thailand last week, killing 14 people.
The storm later gained intensity over the Bay of Bengal, where it hit India’s Andaman and Nicobar Islands, forcing the evacuation of nearly 2,800 tourists over the weekend.