The 5,000-1 outsiders beat bigger rivals Tottenham, Arsenal, Manchester City, Manchester United and Chelsea to land their first top-flight title.
"It's probably the biggest sporting story ever and the biggest sporting achievement ever," Scudamore said.
"Nobody saw it coming and even when it was halfway through the season nobody said it could be sustained."
Scudamore, who negotiated next season's record £5.1bn television rights deal, added in an interview with BBC Sport that "Leicester 2016" would stand as a landmark moment in British sport.
"We don't know what the future holds because we've all become completely hopeless at predicting anything, including the bookmakers and everybody else - because this one nobody saw coming," he said.
|Selby, World Snooker Champion|
"If the bookmakers had it as a 5,000-1 event, you would imagine you should achieve these type of things once every 5,000 years. It gives us 10, 20, 30, 40, 50 years of being able to say: 'Leicester 2016. Just remember Leicester 2016.'"
The Foxes were crowned Premier League champions on Monday, when nearest rivals Tottenham drew 2-2 at Chelsea.
It marked the culmination of an incredible run for the East Midlands club, who were only spared relegation last season thanks to a brilliant sequence of results over their final nine games.
"Of course, you can't compare it with other stories," said Scudamore. "You can't compare it with all Sir Alex Ferguson's achievements, you can't compare it with the Sergio Aguero moment, you can't compare it with the Arsenal unbeaten season because they're different things.
"You're comparing apples with pears. But in terms of an overall story, as an overall achievement, it is absolutely the best."
In a related development, Mark Selby who is also from Leicester and a fan of Leicester City won the 2016 World Snooker Championship.
The night earlier, Mark Selby had worn a deep furrow and dark stubble on his ashen face. He had played himself into a walking corpse, so that here on Bank Holiday Monday he could lift high the World Snooker Championship trophy.
His wish came true at 10.07pm – a doddle compared to the 12.23am finish on Sunday. It was, as if fate had decreed it, only 10 minutes after his team, Leicester City, won the Premier League title.
There have been more free-flowing spectacles in the history of sporting endeavour than Selby’s 18-14 victory over China’s Ding Junhui, but for sheer bloody-mindedness this was a fine performance. It was attritional, tactical, cautious. It was also methodical, unflinching, precise.