Gautam Gambhir, captain of the Kolkata Knight Riders, led celebrations as the players took an open-top bus tour through a sea of frenzied fans to the team's home ground at the Eden Gardens stadium.
Crowd barriers were pushed aside and streams of people broke through police cordons, as officers struggled to prevent the stadium from becoming dangerously congested for the free-entry event.
Officials said 60,000 people were in the packed venue, with another 30,000 locked outside.
The Knight Riders' victory on Sunday was their first success in the IPL, an annual Twenty20 tournament which pulls in huge audiences across India with its blend of hard-hitting cricket and Bollywood-style entertainment.
"It was a dream victory. They have made us proud," said Partha Tripathi, 50, a manager at the United Commercial Bank who took the day off work to enjoy the party.
"I want to be a witness to the epic celebration that the team deserves," he said as he lined up to enter Eden Gardens.
Mamata Banerjee, the chief minister of West Bengal state, of which Kolkata is the capital, met the players and posed with the golden IPL trophy that the team won with just two balls to spare in the final.
Shah Rukh Khan, leading Bollywood actor and the enthusiastic co-owner of the Kolkata Knight Riders, added celebrity glamour to the occasion as confetti was fired into the air.
"We have been waiting for this day so long," he told crowds. "Thank you Kolkata. Thank you West Bengal on behalf of every member of the team. Only Kolkata will rule."
Accompanied by loud music and dancing, the team completed a lap of honour in the stadium to complete the celebrations.
