FIFA president Gianni Infantino echoed the most common and apt description of the "beautiful story" as a "fairytale" after the 5,000-1 outsiders, who performed a miraculous escape from relegation last season, were crowned champions on Monday.
Leicester's first top-flight title was secured after their only remaining challengers Tottenham Hotspur were held to a 2-2 draw at Chelsea when needing to win to keep the race alive.
Ex-Leicester and England striker Gary Lineker said: "LeicesterCity have won the Premier League. The biggest sporting shock of my lifetime, and it's only my team."
TV presenter Lineker had promised to front BBC's ‘Match of the Day’ in his underpants if his old club won it but few people thought he would ever have to go through with it, even when they opened a seven-point lead with two months remaining.
"All season long people kept saying they’ll lose the next one, lose the next one but they kept winning and churning out results," said Chelsea skipper John Terry after the outgoing champions' fightback from 2-0 down ended Spurs' hopes.
"To do what they’ve done this year has been unbelievable and given hope to the smaller teams."
Chelsea fans, who have a soft spot for Ranieri despite him being sacked 12 years ago after owner Roman Abramovich arrived, chanted his name as the clock ticked down on his first top-flight title in nearly 30 years of coaching around Europe.
"It’s an amazing feeling and I’m so happy for everyone," said 64-year-old Ranieri, who was appointed before the start of the season to succeed Nigel Pearson.
"I never expected this when I arrived. I’m a pragmatic man, I just wanted to win match after match and help my players to improve week after week. Never did I think too much about where it would take us.
“The players have been fantastic. Their focus, their determination, their spirit has made this possible. Every game they fight for each other and I love to see this in my players. They deserve to be champions.”
His squad gathered to watch the game at the home of striker Jamie Vardy, named Footballer of the Year earlier on Monday, and video phone footage posted by defender Christian Fuchs showed them exploding with joy at the final whistle.
Captain Wes Morgan, the personification of their astonishing 12-month transformation, said it was their indomitable team spirit that saw them through.
"Everyone’s worked so hard for this, nobody believed we could do it, but here we are, Premier League champions and deservedly so," Morgan told the club website (www.lcfc.com).
Morgan, who spent 10 years in the lower divisions with NottinghamForest and tasted the Premier League for the first time aged 30 last season, added:
"I’ve never known a spirit like the one between these boys. We’re like brothers. People saw it last season when everyone expected us to be relegated, but we fought back to prove people wrong.
"We’ve built on the momentum, but I don’t think anyone believed it would come to this.
“Saturday can’t come quickly enough. I can’t wait to get my hands on the trophy,” added the centre back, who will hoist it in front of the club’s fans in the home game against Everton.
Vardy, who has been transformed from a shot-shy striker last season into an England international, said: "It’s the biggest achievement in the history of a great club and we all feel privileged to be part of it.
"It’s even more special to have done it with these lads. Every minute of hard work we’ve put in on the training pitch has been worth it for this moment.”
Midfielder Andy King added: “I thought I’d seen everything with this club, but I never thought I’d see this.
"The story of where this team has come from to get to this point has been all over the world recently and I think the lads deserve great credit for the way they’ve taken it in their stride, stayed focussed and kept delivering results -- especially with a great side like Spurs chasing us so hard."
Tottenham boss Mauricio Pochettino, who must have thought the race would go into the final two games when his side led 2-0 at halftime on Monday, said: "First of all I congratulate Leicester and Claudio Ranieri and his players and supporters. It was a massive season for them -- we just need to be stronger next season.”
ManchesterCity captain Vincent Kompany said: "Congratulations to the new Champions of England, LeicesterCity. Respect."