The India Meteorological Department (IMD) rated Titli as a "very severe cyclonic storm" that could pack gusts of up to 165 kph by the time it makes landfall early on Thursday.
The IMD warned the cyclone is likely to uproot trees, power and communication poles, destroy coastal houses with thatched roofs, and damage roads, crops and plantations. It also issued a storm surge warning and said it expects low-lying areas in Odisha and the neighbouring state of Andhra Pradesh to be inundated.
At least 300,000 people have been evacuated from the low lying areas of five coastal districts in Odisha state.
The Odisha Chief Minister's office in a tweet said schools and colleges across the state would remain closed for the next two days.
"Operations at Paradip port have been suspended and all ships have been shifted to deep sea," the Deputy Conservator of Paradip Port Captain AK Mohapatra told Reuters.
"All ships have been removed from the harbour," he said.
Indian Railways in a statement said it had cancelled several trains and a senior official at the Biju Patnaik International Airport (BPIA) in the state capital Bhubaneswar said several flights had also been cancelled.
The Bay of Bengal often witnesses cyclones at this time of year, and some have led to widespread death and destruction. The state of Odisha was last month hit by the low-intensity cyclone Daye.