The Foxes' automatic promotion back to the Premier League had already been confirmed after Leeds United were thumped 4-0 by Queens Park Rangers on Friday night.
Jamie Vardy scored twice in the first half before Kasey McAteer netted a third in the 67th minute.
Leicester's title win marks the fourth straight season that the Championship has been won by a team that had been relegated from the Premier League in the previous campaign.
They also become the most successful team in Championship history, winning the competition for the eighth time - beating Manchester City's previous record of seven second-tier titles.
Speaking immediately after his two goals helped secure Leicester's victory on the night, Vardy told Sky Sports the achievement felt "unbelievable".
"It's unbelievable. We knew it was going to be a tough game but we got the job done," the forward said after taking his league tally to 16 goals this season.
"How could you not love scoring goals, especially the second one, scoring in front of the fans - you can't get a better feeling than that. Celebrating with the fans is great.
"We had a couple of off games and we needed to get back to doing what we were doing. We had a talk between us and you've seen since it's paid off. We knuckled down and came out firing."
Kiernan Dewsbury-Hall, who has enjoyed a breakout season this year in the Championship, told Sky Sports: "We've been waiting for this moment all season. The fans deserve this moment, it's a long season and they have been there home and away.
"The Championship is the toughest league in the world. I am going back to the Premier League a better player.
"The goal going into the season was to lift the trophy at the end of it."
Harry Winks - who joined the club in the summer from Tottenham - said he has loved his time in the Midlands so far.
"It's been incredible, it's been tough, it's been amazing, it's been difficult, it's been physical, everything you can think of.
"I've loved every minute of it. I'm happy for everyone at this club, it's a special club.
"We've been celebrating since Friday, so we needed to focus the last couple of days. We went into this game very relaxed and in a nice frame of mind. We've enjoyed it."
Leicester can now reach 100 points for the campaign if they claim a victory in their final game against Blackburn on Saturday, where they will also get their hands on the trophy.
Leeds and Ipswich are left to vie for the last remaining automatic promotion spot, sitting in second and third place respectively.
Read our full report and get all the match stats here with Flashscore.
