The deep depression, formed over north west Bay of Bengal, crossed the Orissa coast near Puri on Friday morning, the meteorological office said.
The system hit the coast between 0530 and 0630 hours and subsequently lay centered close to the temple town.
It was likely to move in a west-nor'westerly direction and weaken gradually, the sources said.
The weather office forecast rain or thundershower over most places of Orissa and heavy to very heavy rain at a few places besides extremely heavy falls (of 25 cm or more) at isolated places in south Orissa during the next 24 hours.
Jeypore town in Koraput district had already experienced a cloudburst on Wednesday night when it received 27 cm of rainfall in a few hours.
Local cautionary signal number three had been kept hoisted at Gopalpur, Puri, Paradip and Chandbali while fishermen had been advised not to venture into the sea which would continue to be very rough to high.
Squally weather with wind speed reaching 55-65 kmph was likely to prevail along and off the Orissa coast, the sources said.