Residents broke into celebrations on the stroke of midnight, with a fireworks display lighting up the skies over the city.
India's new Prime Minister Narendra Modi was among the first to congratulate Rao, promising his "complete support to the people & Government of Telangana" in a message on Twitter.
"India gets a new state! We welcome Telangana as our 29th state. Telangana will add strength to our development journey in the coming years," Modi added.
"Telangana's birth comes after years of struggle and sacrifices by several people. We pay our respects to them today."
Telangana has been created by splitting the state of Andhra Pradesh in two. Hyderabad, an IT hub, will serve as the capital of both states for the next decade.
The campaign to create a separate state in one of Ind