At least 1,000 homes have been destroyed and entire villages submerged in Bangladesh.
Five people have been confirmed dead and at least 63 were injured.
After a million people were evacuated to safety, Bangladesh’s director of Meteorological Department said “fear of a major disaster is mostly over”.
The cyclone weakened as blew north-eastwards from India into Bangladesh on Saturday, but remained very powerful, enough to destroy dozens of villages on the low lying coast.
Gusts of up to 43mph were recorded.
Houses were also destroyed in the district of Noakhali, where two children aged two and 12 were killed, and 30 adults were seriously injured.
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India also evacuated more than a million people to avoid Cyclone Fani.
A least 16 people were killed by the cyclone when it struck India on Friday 3 May, but officials said the death toll could have been significantly worse.
In 1999, a major cyclone in the Bay of Bengal ravaged the coast of Orissa for 30 hours and killed more than 10,000 people.
Cyclone warning systems have improved since, allowing authorities more time to evacuate people.
Orissa’s chief minister said the cyclone of 1999 was one of the largest evacuations in human history.