The 5000-1 outsiders won the first top-flight title in their 132-year history on Monday when challengers Tottenham could only manage to draw with Chelsea.
O'Neill, who led the club to two League Cup wins, said the remarkable rise "will live long in the memory".
"Personally, I don't think we'll see it in our lifetime again," he added.
The Republic of Ireland boss said Leicester's achievement rekindled memories of his involvement in Nottingham Forest's glorious run under Brian Clough in the late-1970s.
"It's the greatest achievement, obviously, of the century, although that's just 16 years old," the former Northern Ireland international said.
"And I think since Nottingham Forest away back in 1977-78, when I was a member of the team that came up from the old second division and won the [top division] at the first time of asking, this is the greatest achievement since then."
O'Neill, who managed Leicester from 1995 until 2000, was full of praise for the Foxes' boss Claudio Ranieri for guiding the club to glory after they were tipped for relegation at the start of the season.
"Ranieri deserves all the credit in the world, the players have been simply sensational, the owners have been terrific as well," he said.
"It's been a great story.
"Everything about it - from away back last year when they just avoided relegation, to this magnificent rise - it has been incredible and so romantic."
Gerry Taggart, the former Northern Ireland centre-half who played almost 150 games for Leicester, said he hoped the club's triumph would change English football "for good, for the better".
"I've been saying for the last six or seven weeks that I believed Leicester would go on and win the title," he said.
"I've watched a lot of this team this season and it's just mind-blowing the way they've got to where they are.
"The way they play football is good for the game."
Taggart returned to Leicester in a coaching role after his playing career and had a brief spell as caretaker manager, and he said the way in which the club is run has helped drive it to success.
"The backroom staff at Leicester City are first class, they've spent a lot of years trying to perfect what goes on behind the scenes," he said.
"This is as much about them as it is about the players or the manager, to be honest."
Taggart gave credit to Ranieri for his man-management skills that helped to draw odds-defying performances from his players, most of whom had never before come close to reaching these heights.
"He simplified the game for them, let them go out, express themselves when they've got the ball," Taggart added.
"But it's been especially good to see when they haven't got the ball everybody is contributing to the side.
"That's what has got them over the line - pure and simple teamwork."
Leicester City's crowning as Premier League champions is an "incredible and romantic" story, the club's former manager Martin O'Neill has said.