The Gers were two points behind their neighbours heading into the last round but a stunning late recovery by Motherwell against the Hoops allowed Alex McLeish's men to clinch the title.
Rangers had arrived at Hibernian knowing they had to win to have any chance of overhauling Celtic and Nacho Novo's 59th-minute strike – his first goal for more than two months – provided that victory.
And, as Rangers and Hibs played out a scoreline at Easter Road that would also ensure UEFA Cup football for the home side, thousands of ears instead became glued to radios in the hope of good news.
Martin O'Neill's Celtic appeared to have things firmly under control at Fir Park when Chris Sutton put them in front in the 29th minute and few had expected them to surrender their lead.
However, Terry Butcher's side staged an astonishing late rally, with Scott McDonald equalising in the 88th minute to put Rangers back in the driving seat.
McDonald, an Australian who had a Celtic-supporting father and a Rangers-supporting mother, then struck again in injury time when he cut inside and hit a shot which took a deflection and spun over goalkeeper Rab Douglas.
News of Celtic's 2-1 defeat sparked scenes of jubilation at Easter Road as Rangers rejoiced in recapturing the title in the most dramatic of circumstances.