Brendan Rodgers’ side needed three points against fifth-placed Hearts to be confirmed as champions after Aberdeen hammered Dundeeon Friday.
And they did so with a hat-trick from Scott Sinclair and goals from Stuart Armstrong and Patrick Roberts.
Unbeaten Celtic have dropped just four points so far during their campaign.
“My job when I came in was to win it in the best way we possibly could,” said Rodgers.
“We have had many outstanding performances, but we have only just begun because there’s still an awful lot of development in this team. That’s the real exciting part.”
Celtic are still on course to win the domestic treble, having beaten Aberdeen in November to win the League Cup, while they face rivals Rangers in the Scottish Cup semi-finals later this month.
The last time the club won all three major Scottish domestic trophies in one season was 2000-01 and the feat has only been achieved once since – when Rangers claimed a treble in 2002-03.
“The run we’re on is incredible,” said Rodgers in an interview with Football Focus prior to Sunday’s title-clinching victory.
The last time a Scottish side went a full season unbeaten was Rangers in 1898-99, while Celtic did the same the year before – but the season only lasted 18 games.