Captain Darren Sammy hopes winning the World Twenty20 title will inspire West Indies to "start something special".
A 56-ball 78 from Marlon Samuels helped West Indies recover from a poor start and set up a
"This is the start of something special for the West Indies team and the fans back home," said Sammy.
"We won't say 'we're back'. Hopefully it's a step in the right direction and we've made the people proud. I'll always cherish this moment."
West Indies, the dominant team in international cricket from the late 1970s through to the 1990s, celebrated wildly in Colombo as they won their first major competition since the 2004 Champions Trophy.
"Throughout the last two years we've shown a never-say-die attitude," added Sammy, who made an unbeaten 26 from 15 deliveries in a total of 137-6 which looked unlikely when they were 32-2 after 10 overs.
"I've got to thank the Almighty, and thank everyone who's ever supported West Indies - this is for the fans.
"The team has been through a lot for the last decade. We left home with 'one team, one people, one goal', and the belief we left the Caribbean with took us through.
"I know it'll be a party from Jamaica down to Guyana. Thankfully it's Sunday as if it were a weekday nobody would be at work."
Sri Lanka seemed in control as they restricted West Indies' batsmen, with Chris Gayle taking 16 balls to reach three.
But an inspired Samuels hit six sixes and three fours to shift the balance of power, before Sri Lanka were bowled out for 101 in the 19th over.
Man of the match Samuels, who was suspended from the game for two years for passing on team information to a bookmaker in 2007, described the victory as a moment which would "live forever".
"Two years and I'm back. I can't explain how much this means to me," said Samuels, who also took 1-15 from his four overs.
He added: "My career has had its ups and downs - a lot of tough times but I'm not someone that will ever give up.
"The person that I am deep down inside is the reason I'm still here playing cricket.
"I have a family that believe in me. So if outsiders don't, that doesn't really matter to me.
"Being under pressure on a cricket field is nothing compared to what I've been through off the field."