Authorities said the cyclone crossed the coast between Nagapattinam and Vedaranyam districts between 12.30 a.m. and 2.30 a.m. with wind speeds of about 110-120 kmph.
So powerful were the gales that the roof sheets of the Nagapattinam railway station were damaged.
Chief Minister K. Palaniswami said in Salem, some 350 km from here, that 11 persons had lost their lives due to the cyclone.
He said a sum of Rs 10 lakh would be paid to each family of the dead. For those severely injured, a sum of Rs 100,000 would be paid and those who suffered minor injuries would get Rs 25,000.
About 82,000 people living in low-lying areas were sent to 471 relief centres, the Chief Minister said, adding that the preventive measures helped keep the death toll low.
Relief centres were set up in Cuddalore, Nagapattinam, Ramanathapuram, Thanjavur, Pudukottai and Thiruvarur on Thursday itself.
The India Meteorological Department (IMD) has forecast rains till Friday evening.
R.B. Udhyakumar, Minister for Revenue and Disaster Management, said all the trees felled by the cyclone were being removed.
Road traffic was hit in Nagapattinam due to the fallen trees.
The government snapped power supply on Thursday night as precaution. The cyclone damaged some 12,000 power poles.
Several universities in Tamil Nadu have postponed their exams slated for Friday.
Similarly, schools will remain closed on Friday in Nagapattinam, Cuddalore, Thanjavur, Pudukottai, Thiruvarur and several other districts in Tamil Nadu and in Puducherry including Karaikal.
Isolated rains are likely over north Tamil Nadu, Puducherry, north Kerala and interiors of south Karnataka.
Gale wind speed reaching 100-110 kmph gusting to 120 kmph very likely in central parts of Tamil Nadu and Puducherry coasts during next six hours.
Powerful winds are also likely in the remaining parts of Tamil Nadu and the Palk Strait, which divides Tamil Nadu and Sri Lanka.
According to the Chief Minister, the Fisheries Department will estimate the damage to the fishing boats before paying compensation to the fishermen.