0427 GMT June 21, 2021
Eleven people, mostly fishermen, remained missing in the two countries as nearly 9,000 people sought shelter in relief camps, AFP reported.
Scores of localities suffered flooding and cut power and telephone lines as winds of up to 130 kilometers (80 miles) per hour swept the region.
Weather experts warned of more heavy rains to come, as the water level rose in several rivers in southern India.
The tiny Indian island of Lakshadweep off the country's western coast braced for winds of 145 kilometers (90 miles) per hour.
The Sri Lankan disaster management center said 77,000 people in 16 districts have been affected, with the highest number in the southern Galle district.
Nearly 4,000 people are in Sri Lankan relief camps amid widespread destruction of property.
Authorities are on red alert in coastal areas, with five deaths already reported in Kanyakumari on the southern tip of India.
Schools and colleges in parts of India's southern states have been shut as authorities try to restore nearly 4,000 snapped power lines.
The Kerala state emergency department said nearly 3,200 people were in relief camps. "Seven people died in several incidents and 218 were rescued from the sea," an agency official told AFP.
Weather officials said the storm was likely to move north into Tamil Nadu and the east coast state of Andhra Pradesh in the next four days.
India's eastern coast – including major cities like Chennai and Bhubaneswar – are prone to storms that wreak immense damage between April and December.
In 1999, more than 8,000 people were killed when a cyclone battered the eastern state of Orissa.
While Cyclone Ockhi was said to be weakening, another tropical storm was brewing in the Bay of Bengal on the east coast, officials said.