The Very Severe Cyclonic Storm Yaas made landfall between the coasts of Odisha's Bhadrak and Balasore district on Wednesday.
Along with heavy rains, Yaas brought in high-speed winds with gusting speeds of 130-155 km/h.
At least four people reportedly died due to the cyclone; three in Odisha and one in West Bengal.
The Indian Navy and the Indian Coast Guards along with the NDRF have been engaged in relief and rescue efforts in Odisha and West Bengal.
High tide caused by the cyclone led to the Ganga swelling and flooding its banks.
West Bengal CM Mamata Banerjee said that one crore people had been affected by the cyclone with more than three lakh houses suffering damage.
Odisha CM Naveen Patnaik said that families of 128 villages in the affected districts will be provided with seven days worth of ration and other supplies.
As Yaas moved inland towards Jharkhand, the state government evacuated 12,000 people to safe zones and imposed total lockdowns in some areas to prevent people from moving outside.