A Joe Lewis own goal put Steven Gerrard's champion side ahead at Ibrox, with a Kemar Roofe double and an effort from veteran striker Jermain Defoe completing a dominant victory that took the Glasgow giant up to 102 points.
Gerrard's side emphatically halted Celtic's bid for 10 consecutive top-flight crowns and, in going an entire campaign unbeaten, matched the exploits of Brendan Rodgers's Bhoys in 2016-2017.
Rangers' 55th Scottish title overall has proved to be a record-setting affair, with a miserly 13 goals conceded – one fewer that the previous best by Celtic back in 1913-1914.
Despite Aberdeen's spirited efforts after half-time, Allan McGregor was able to keep a clean sheet, the Gers' 26th shutout this term to match Celtic's 107-year-old record.
Victory also meant a perfect return of 19 wins from 19 at Ibrox in 2020-2021. That matched the feat achieved by Martin O'Neill's Celtic, which eventually chalked up 26 in succession at Parkhead between 2002 and 2004.
"It's been a while since I've had the smell of champagne. It's been so long I'm actually enjoying it," a sodden Gerrard said during the post-match celebrations.
"I'm so proud of the boys and all the staff around it, but the main thing is the supporters. I was asked to come here at a difficult time, it had been even more difficult before that.
"I have to pay my respects to the people who got it to the point where I took over. After that it was about having a vision, getting the right people in the right places, the right support from the board and fighting for it.
"We've fought every day for the last three years to get to this point."
Celtic concluded an utterly wretched season, one that brought about the sacking of manager Neil Lennon, with a 0-0 draw at Hibernian to finish 25 points shy of its bitter rival.