Ranieri, 65, guided the Foxes to the title despite them being rated 5,000-1 shots at the start of the campaign.
Leicester are one point above the relegation zone with 13 matches left.
“After the euphoria of last season and being crowned champions, all I dreamt of was staying with Leicester. Sadly this was not to be,” Ranieri said.
“The adventure was amazing and will live with me forever. My heartfelt thanks to everybody at the club, everybody who was part of what we achieved, but mostly to the supporters.
“You took me into your hearts from day one and loved me. I love you too.
“No-one can ever take away what we achieved together and I hope you think about it and smile every day the way I always will.
“It was a time of wonderfulness and happiness that I will never forget. It’s been a pleasure and an honour to be a champion with all of you.”
Ranieri’s departure came less than 24 hours after Wednesday’s 2-1 defeat at Spanish side Sevilla in the first leg of their Champions League last-16 tie. The second leg is on 14 March.
On Saturday, Leicester were knocked out of the FA Cup by League One Millwall.
In explaining the club’s decision, vice-chairman Aiyawatt Srivaddhanaprabha said “long-term interests” had been put above “personal sentiment, no matter how strong that might be”.
The Foxes took last season’s Premier League title by 10 points but have won just five top-flight games this season, and could become the first defending champions since 1938 to be relegated.
They have lost their past five league matches and are the only side in the top four English divisions without a league goal in 2017.
Speaking earlier on Friday, Leicester caretaker boss Craig Shakespeare denied a player revolt led to Ranieri’s sacking.
BBC Sport understands some players were summoned to meet the chairman after the defeat by Sevilla, and Ranieri’s fate was sealed by the negative reaction.
“There was a lot of frustration because of the results, but he had not lost the dressing room,” Shakespeare said.
“A lot of the talk of unrest has been speculation. I’ve not had one problem with the players.
“I always feel sorry when people lose their jobs. My relationship with Claudio has been fine all along.
“I spoke to him last night and he thanked me for my support throughout. It was not brief and we exchanged views. A lot of what we said will stay private.”
Shakespeare and first-team coach Mike Stowell will take charge of the squad until a new manager is appointed.
Ranieri’s compatriots Paolo Benetti and Andrea Azzalin, both key members of his coaching staff, have left the club.
Who might replace Ranieri?
Ex-Manchester City and Inter Milan boss Roberto Mancini and Nigel Pearson, who Ranieri replaced in 2015, are the early bookmakers’ favourites to take over at Leicester.
Former Birmingham boss Gary Rowett – a one-time Foxes player who is around fifth favourite – told BBC Radio 5 live: “I’m sat at home waiting for the right opportunity to come along. Leicester would be an amazing one, but it’s still raw for everyone.”
Rowett, who played for Leicester between 2000 and 2002, was controversially sacked by Birmingham in December, and replaced by former Chelsea striker Gianfranco Zola.
“I played there for two years so I’ve had good experiences at Leicester and it’s an excellent club. It would be a daunting one for anyone and a fantastic opportunity for someone,” he added.
Ranieri’s statement in full
Yesterday my dream died.
After the euphoria of last season and being crowned Premier League champions, all I dreamt of was staying with Leicester City, the club I love, for always.
Sadly this was not to be. I wish to thank my wife Rosanna and all my family for their never-ending support during my time at Leicester.
My thanks go to Paolo and Andrea, who accompanied me on this wonderful journey. To Steve Kutner [Ranieri’s agent] and Franco Granello [his Italian agent] for bringing me the opportunity to become a champion.
Mostly I have to thank Leicester City Football Club. The adventure was amazing and will live with me forever.
Thank you to all the journalists and the media who came with us and enjoyed reporting on the greatest story in football.
My heartfelt thanks to everybody at the club, all the players, the staff, everybody who was there and was part of what we achieved. But mostly to the supporters. You took me into your hearts from day one and loved me. I love you too.
No-one can ever take away what we together have achieved, and I hope you think about it and smile every day the way I always will.
It was a time of wonderfulness and happiness that I will never forget. It’s been a pleasure and an honour to be a champion with all of you.
By Andrew for KTV Sierra Leone.