A Jan Vennegoor of Hesselink header was enough to give Celtic the points with Rangers needing to win by five goals at Pittodrie to match their rivals' superior goal difference.
It caps a memorable comeback for Celtic who at one stage lagged seven points off the pace. But a fine run of form - winning their final seven games - hauled back their rivals who ran out of steam after a gruelling season. And captain Stephen McManus was delighted to prove the doubters wrong.
"Six or seven weeks ago there was folk all over the country written us off, but we always believed we could do it and its been great to prove everybody wrong," he said.
"There's nothing better in football than proving people wrong. It's just brilliant for everyone."
After becoming the first Celtic manager since Jock Stein to win three back-to-back titles, Gordon Strachan was full of praise for his team.
"This has been one of the most fantastic occasions in my life," beamed Strachan.
"We have a bunch of guys who believed here."
After seeing their quadruple dreams shattered in the last eight days, Rangers will now have to console themselves with the prospect of a domestic cup double when they face Queen of the South in Saturday's Scottish Cup Final.
