Virat Kohli hit a match-winning 76 to set up India's seven-run win over South Africa in a thrilling final in Barbados on Saturday, before he and Rohit announced their retirement from T20 internationals.
The title victory comes after more than a decade of heartbreaks in knockout matches of International Cricket Council (ICC) tournaments and their last crown at the 2013 Champions Trophy.
The cricket-crazy country erupted with midnight celebrations as fans in blue Indian shirts on cars and bikes took to the streets across cities including the capital New Delhi.
"One Nation, One Joy," blazed the front page of the Times of India newspaper.
"Finally, India's final," said the Indian Express daily.
Mahendra Singh Dhoni, India's captain for their first T20 World Cup triumph in 2007, praised the team for holding their nerve in a tense finale.
"Word Cup Champions 2024. My heart rate was up, well done on being calm, having the self-belief and doing what you guys did," Dhoni wrote on social media.
"From all the Indians back home, and everywhere in the world, a big thank you for bringing the World Cup home."
'Starry-eyed children'
Indian Prime Minister Narendra Modi on Sunday said he had spoken to the team, congratulating them on their "excellent skill and spirit", he wrote on social media.
Rohit was "excellence personified," said Modi, who praised his "aggressive mindset, batting and captaincy", while thanking coach Rahul Dravid's "unwavering dedication (and) strategic insights."
He also offered India's thanks to Kohli, who he said had "shone in all forms of the game".
"T20 cricket will miss you but I am confident you'll continue to motivate the new generation of players."
Rohit's team came close to ending India's title drought last year, losing to Australia the final of the World Test Championship and the 50-over World Cup.
But in a clash of the tournament's two unbeaten sides in Barbados, India held their nerve to defend 176 while South Africa choked when needing 30 off 30 balls to win their first World Cup.
"Every star added to the Team India jersey inspires our nation's starry-eyed children to move one step closer to their dreams," batting great Sachin Tendulkar, who won the 2011 World Cup under Dhoni, wrote on social media.
"Life comes full circle for Indian cricket in the West Indies -- from our lows in the 2007 ODI World Cup, to becoming a cricketing powerhouse and winning the T20WC in 2024."
Former captain Sourav Ganguly offered his "heartiest congratulations to Rohit Sharma and his team" on social media.
"What a game to win," he said. "The talent the country has, they will win many more."
Kohli's 59-ball knock, pace spearhead Jasprit Bumrah's figures of 2-18, Hardik Pandya's last over to defend 16 runs and a stunning catch on the boundary by Suryakumar Yadav were the outstanding memories of a thrilling final.
Michael Vaughan, the former England captain, rated Bumrah as the "greatest ever white ball seam bowler" and India as the "best team".
