Concerns had been raised by the Pakistan Cricket Board over threats from Hindu extremists, who attacked the offices of Indian cricket's governing body last year.
However, PCB chairman Shaharyar Khan said on Thursday that the team had been cleared to play in March and April.
"I am pleased that our government has given its consent," said Shaharyar.
"As a duty of care, we have asked [world cricket governing body] the ICC to put in place special arrangements for the Pakistan cricket team while in India."
India and Pakistan have not played a Test series since 2007 due to fallout from the terrorist attacks on Mumbai in 2008, blamed on militants based across the border.
Since 2009, Pakistan have played their 'home' Test series in the UAE after a terrorist attack on the visiting Sri Lankan team led to a boycott on tours to the country.
The World T20 runs from 8 March to 3 April.
Pakistan are scheduled to play a qualifier team on 16 March in Kolkata, then hosts India on 19 March in Dharamsala.

Firefighters spent several days at the site in Duncan Street following the blaze on 2 March, which reduced train services and caused travel delays.
The Environment Agency (EA) suspended Recovered Fuels Shipping Limited from accepting waste after the fire.
The firm was "broadly compliant" with fire safety law, the fire service said.
Recovered Fuels Shipping Limited, whose site was run by Asset and Land Group, could not be contacted for a comment. It has until 7 August to appeal the decision.
Greater Manchester Fire and Rescue Service (GMFRS) visited the premises nine times in the last 12 months.
Geoff Harris, GMFRS area manager, said: "The site operators, Asset and Land, have been broadly compliant with fire safety legislation throughout that time."
The fire service raised concerns to the EA in February over the impact a fire could have on nearby residents, transport and the environment.
"The EA were very interested in our concerns, which resulted in our fire safety officers conducting joint visits to the site with EA staff, the EA decided to take enforcement action against the site operators," Mr Harris said.
An EA spokesman said: "After consideration of all the facts relating to the company and the site, the EA has now decided to revoke the environmental permit.
"Subject to any appeal, the revocation takes effect on 7 August, which means after that date the company will no longer be able to operate from that site. The company is still required to remove all the waste."
The cause of the fire remains undetermined.
Pakistan will play in the World Twenty20 after the government approved their participation in India.
[NEXT_CONCEPT]
A company which runs a paper recycling plant in Salford where a major fire broke out has had its environmental permit revoked.