Cyclone Hudhud was expected to make landfall before noon (0630 GMT) packing winds of nearly 200 kilometres (125 miles) per hour.
Thousands of people living in flimsy housing in fishing villages in the eastern state of Andhra Pradesh were among the first to be moved to concrete relief shelters, officials said.
Arvind Kumar, a state government official in Andhra Pradesh, where the storm will hit first, said 300,000 people had been evacuated there.
"We are trying to minimise the movement of people," he said as the storm gathered strength over the Bay of Bengal.
"Six hours after landfall will be very crucial, though the wind speeds will come down to about 100 kilometres (per hour) by then."
Prabhat Mohapatra, deputy relief commissioner for the neighbouring state of Orissa, said nearly 50,000 people had been evacuated from there.
"Some are being evacuated this morning," he told Indian broadcaster NDTV.
"We are worried about flooding here (Orissa) and have depleted our water reservoirs by 50 per cent."