There have been protests in Andhra Pradesh for many days
The Indian government is to allow a new state to be carved out of part of the southern state of Andhra Pradesh.
Home Minister P Chidambaram said the process of forming Telangana state would begin soon. Campaigners say the region has long been neglected.
Supporters of the state are celebrating after days of violent protests. One of their leaders ended a hunger strike.
But many in India fear acceding to the protesters' wishes could fuel demands for other new states across India.
Dozens of Andhra Pradesh assembly members and at least one Indian MP with a seat in the state have announced they are resigning in protest at the move.
Analysts say the flurry of resignations, mostly from the governing Congress party, could lead to a political crisis in Andhra Pradesh.
Correspondents say Telangana state is likely to include one of India's major software hubs, Hyderabad.
The city, currently the Andhra Pradesh capital, is home to leading world companies in India like Microsoft and Google.
The government announcement came at midnight on Wednesday.
"The process of forming the state of Telangana will be initiated. An appropriate resolution will be moved in the state assembly," Mr Chidambaram said after talks with Prime Minister Manmohan Singh and Congress party leader Sonia Gandhi.
BBC News, Delhi
Many are concerned that the move may open a Pandora's box.
They fear that this will only fuel similar movements in other states and end up significantly redrawing the map of the country.
Already one member of parliament from Andhra Pradesh has resigned in protest over the decision to create Telangana.
The government appears to have given into the demands of protesters, particularly after the leader of the campaign became dangerously ill following a hunger strike to press home his point.
It's clear this is not the last that has been heard on this volatile issue.
On hearing the news, crowds in Hyderabad and nine other districts of Telangana erupted in celebration, reports the BBC's Omer Farooq in the state capital.
Mr Chidambaram said the government had asked for court cases against leaders, students and others "associated with the present agitation" to be dropped.
He also appealed to protesters to call off their demonstrations.
His announcement was greeted with jubilation among protesters, who let off fire crackers, beat drums, danced and sang songs.
Some of the celebrations took place outside the Hyderabad hospital where one of the campaign leaders, K Chandrasekara Rao of the Telangana Rashtra Samiti (TRS) party, had been admitted during his fast.
Mr Rao said: "I am happy that this is the victory of 35 million people who live in the Telangana region."
Protest rallies seeking a separate state planned for Thursday were called off.
Thousands of police had been deployed for the rallies, but after Mr Chidambaram's announcement security was relaxed, our correspondent says.
Telangana region is spread over 10 northern districts of Andhra Pradesh.
INDIA'S NEWEST STATE
Population of 35 million
Formed from 10 districts of Andhra Pradesh, including city of Hyderabad
Landlocked, predominantly agricultural area
One of the most under-developed regions in India
Culmination of 50-year campaign
More than 400 people died in 1969 crackdown
The demand for separate state status for the underdeveloped and drought-prone area dates back 50 years.
More than 400 people died in violence over the demand for a Telangana state in 1969.
Campaigners say Telangana's economic development has been neglected in favour of the richer and more powerful Andhra region - and that a new state is the only solution.
The last three new states in India were formed in 2000: Chhattisgarh was created out of eastern Madhya Pradesh; Uttarakhand was created out of the hilly areas of northern Uttar Pradesh, and Jharkhand was carved from Bihar's southern districts.
India currently has 28 states.