India beat Pakistan in Monday's final in Johannesburg by five runs to clinch their first major trophy since 1983.
The stadium ceremony came at the end of a victory parade through the rain-hit streets of Mumbai.
The team, led by 26-year-old captain Mahendra Singh Dhoni, travelled on an open-top bus, dancing and waving to thousands of ecstatic fans.
"I wish to congratulate the entire team for this historical victory," Indian cricket board chief and federal agriculture minister Sharad Pawar told the ceremony at the Wankhede Stadium.
Thousands of people turned out in drizzle to cheer and welcome the team on the route and inside the stadium.
Television pictures showed the Indian players on the upper deck of the bus waving Indian flags and taking pictures.
Indian batsman Yuvraj Singh was seen dancing on top of the bus.
Thousands of fans stood under umbrellas on the city's roads to greet the team and many ran along with the slow moving bus. People danced, distributed sweets and burst crackers in the city.
"I'm so excited about seeing these guys. They have made India proud," Parag Paranjpee, who missed college to join the celebrations, told the Associated Press news agency.
'Making amends'
The bus carrying the team moved through Mumbai city to the local Wankhede stadium, where the players were met by state government and local cricket authorities.
The victory parade took over two hours, reports said.
The Indian cricket has board announced a bonus of $2m for the team, and a $250,000 cash prize to Yuvraj Singh for his record feat of hitting six sixes in an over, in a match against England.
Captain Mahendra Dhoni has said India's World Twenty20 triumph had made amends for their 50-over World Cup nightmare.
The Indians went out at the first stage in the Caribbean in April but edged out Pakistan in Johannesburg on Monday to be crowned the best team in the world in the game's shortest format.
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