Winds were measured at 200 km/h (125mph) as Cyclone Phailin hit the coast near Gopalpur, Orissa state, at about 21:15 (15:45 GMT).
Authorities had predicted a storm surge of at least 3m (10ft) that was expected to cause extensive damage.
Officials say they are better prepared than in 1999 when a cyclone killed more than 10,000 people in Orissa.
Cylcone Phailin has been classed as "very severe".
The BBC's Sanjoy Majumder reported heavy rain and high winds lashing Gopalpur as the cyclone made landfall.
The storm has ripped up trees and road signs, and cut power supplies in some areas. Five deaths were linked to the cyclone by Indian media.
Officials had earlier said that no-one would be allowed to stay in mud and thatched houses along the coast of Orissa and Andhra Pradesh states.
The army is on standby for emergency and relief operations.
Helicopters and food packages were ready to be dropped in the storm-affected areas.
Cyclone Phailin is expected to be the biggest storm in the region for 14 years
As many as 500,000 people have left their homes, many for storm shelters
The storm was expected to cause extensive damage to coastal areas
Authorities say they are now better prepared than in 1999, when a super-cyclone hit OrissaHours before the cyclone made landfall it was generating winds of 240 km/h (150mph) over the Bay of Bengal.
Sushant Sahoo, a resident of Orissa's state capital, Bhubaneswar, told the BBC that it had been raining there since the morning, and the streets were empty.
"We have no electricity, it is very dark right now and very grim," she said.
"I have dry food and candles. The local government has been good at getting everyone prepared and taking care of people."
India's eastern coast and Bangladesh are routinely hit by cyclonic storms between April and November that cause deaths and widespread damage to property.
In December 2011, Cyclone Thane hit the southern state of Tamil Nadu, killing dozens of people.
Credit to BBC
