The Hoops struck twice late on to earn a 3-1 win and usurp the Jambos, who had led the league for almost the entirety of the campaign.
A fifth consecutive title and 14th in 15 years for Celtic arrived in very different circumstances from the rest.
Used to running away with the league, the Hoops have had to chase down Hearts in a season marked by rancour off the field.
Celtic fans have protested throughout for boardroom change over a perceived lack of investment in the squad.
O'Neill, 74, has twice stepped in to take interim charge after Brendan Rodgers departed in October and Wilfried Nancy lasted just 33 days after six defeats in eight games.
But Celtic produced seven consecutive wins down the final straight to snatch the title once more.
"We made plenty of mistakes, but there is plenty of courage in the team. I'm not talking about physical courage but mental courage, which has carried us over the line," said O'Neill.
"Celtic today, when there is unison in the stadium, it's rocking. They never give up. Maybe I did, but they didn't."
O'Neill added: "This is the most special place on earth.
"When there is unison in this stadium, it is a sight to behold, and obviously, the players have been magnificent."
However, there could be repercussions for the Glasgow giants after supporters spilled onto the pitch after Callum Osmand ran the ball into the net to seal the title in stoppage time.