Favourites India won the title on Saturday after defeating South Africa in a thrilling final, but their travel plans were disrupted by Hurricane Beryl.
"The team has left from Barbados on a special Air India flight," Board of Control for Cricket in India (BCCI) vice-president Rajeev Shukla told the Press Trust of India.
Rohit Sharma's men were scheduled to reach the Indian capital New Delhi on Thursday morning, where they will meet Prime Minister Narendra Modi.
The special flight was arranged after the players were stranded in a hotel for three days after the victory.
Rohit, who announced his T20 international retirement alongside fellow star Virat Kohli after the final, posted a picture of him holding the T20 trophy with teammate Suryakumar Yadav aboard the flight, with a caption "Coming home".
After their meeting with Modi, the team will fly to Mumbai for a victory parade in the heart of India's financial capital, Shukla said.
Last weekend's win ended an 11-year global cricket trophy drought for India following their 2013 Champions Trophy win.
Their last World Cup victory was at home for the 50-over tournament in 2011 under M.S. Dhoni.
The final was the last match in charge for coach Rahul Dravid, 51, who was bounced in the air by the team during the celebrations.
