The cyclone in the Bay of Bengal, called "Lehar", encountered colder air and sea as it approached the coast and has lost much of its energy.
"There's no danger," head of the cyclone warning system in the weather office, M Mohapatra, told AFP by phone.
"It will cross the coast (later Thursday) as a depression. It's a deep depression now."
Sustained wind speeds would be only 45-55 kilometres, down from 120 kilometres an hour on Wednesday.
Some 27,000 people had been evacuated by Wednesday in the state of Andhra Pradesh where the storm was set to make landfall.
Disaster teams were aiming to get another 120,000 villagers into camps as it approached.
The latest cyclone was less serious than Cyclone Phailin which slammed into the coast further to the north in October, killing 18 and leaving a trail of destruction.
Phailin, which was also classed as "very severe", had sustained winds of over 200 kilometres an hour that uprooted trees, overturned trucks, snapped power lines and damaged crops in Andhra Pradesh and its northern neighbour, Orissa.
The most powerful storms which strike India at this time of year are classified as "super-cyclones" followed by "very severe" and then "severe".
Cyclone Lehar comes just a week after Cyclone Helen - a "severe" storm - killed eight people and destroyed large tracts of farmland in Andhra Pradesh.
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