Brendan Rodgers' men beat Rangers 4-0 in the Scottish Cup semi-final two weeks ago but eclipsed that heavy defeat with an even more humiliating thrashing at Parkhead on Sunday.
After a frantic start in a celebratory atmosphere, Celtic took the lead in the 14th minute.
Kieran Tierney bamboozled the Rangers defence on Celtic's left wing and delivered a pinpoint low cross for Odsonne Edouard, deputising for injured star forward Moussa Dembele, to stab home from close range.
Jason Holt forced a brilliant save from Craig Gordon at the other end, the goalkeeper getting down low to his left to keep out the shot, as Rangers briefly rallied.
But that proved brief respite as two superb goals in the space of four minutes before the break wrapped up victory and the title. Edouard raced clear to thump a low drive past Jak Alnwick before James Forrest hit a similar strike after breezing past a series of half-hearted Rangers challenges.
Despite Alnwick's excellence, Celtic were rampant after the interval and Tom Rogic extended the lead with a placed finish from outside the box in the 47th minute, before Callum McGregor slotted in Edouard's pass for the fifth.
Liverpool legend Steven Gerrard has been linked with taking over at Rangers to face off against his old boss Rodgers next season, but on this evidence the gap between the Old Firm rivals is a gaping chasm.