Buildings were illuminated, people exchanged sweets and congratulated one another after the union cabinet's approval on Thursday.
"It is a moment of pride and glory for all the Odias," Chief Minister Naveen Patnaik said.
He said the decision will help create opportunity for the state to carry out more research and development of its language.
Patnaik said government buildings across the state will stay illuminated with colourful lights for three days while schools and educational institutions would organise special programmes to mark the occasion.
The Odisha Sahitya Akademi, the state's apex literary organisation, has also planned to organise a special function.
With the union cabinet approving the proposal, Odia became the sixth language of the country to get the classical language status. The other languages in the same league are Sanskrit, Tamil, Telugu, Kannada, and Malayalam.
The approval came about a fortnight after Chief Minister Naveen Patnaik wrote to union Culture Minister Chandresh Kumari Katoch to take steps for considering the proposal.