Second-half goals from Leigh Griffiths and Stuart Armstrong secured the victory for the Glasgow club and made sure they ended the campaign with 34 wins and four draws.
Celtic, who have already won the Scottish League Cup, remain on course for a domestic treble ahead of next Saturday's Scottish Cup final against Aberdeen.
They are the first champions to go an entire campaign without defeat since Glasgow rivals Rangers, who won all 18 league matches in 1899.
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"It's an incredible achievement. I am a Celtic supporter so I know what it feels like. The fans' enjoyment is the most important thing for me and I think they have a good feeling," said former Liverpool manager Rodgers.
"You come in and plan to win. However, to perform like we've done is truly remarkable. The club is very much together as one.
"The group have worked so hard for all the records they have broken, and they thoroughly deserve it. It's been a great season," he added.
Having clinched their sixth consecutive title in April, Rodgers's side took their points tally for the season to 106 -- breaking the club record of 103 set 16 years ago.
There was a vibrant and celebratory atmosphere at Celtic Park with the 50th anniversary of Celtic's European Cup triumph against Inter Milan, in Lisbon in 1967, marked before the game.
Despite the singing and stunning stadium-wide tribute to the 'Lisbon Lions', there was a lack of intensity from the home side in the opening 45 minutes.
But the brighter second-half display, inspired by some impressive wing play from the 20-year-old Patrick Roberts, ensured the 60,000 capacity crowd could fully enjoy the Premiership trophy celebration.
Griffiths's well-taken header equalled the club's previous best of 105 goals for a single campaign while Armstrong's second -- a rebound after Scott Sinclair's effort fell into his path -- set another record.
Their 30-point winning margin over second-placed Aberdeen, who won 6-0 at Partick Thistle on the final day, is also a record, breaking the previous 29-point gap set by Neil Lennon's side in 2013-14.
(Additional reporting by Ed Dove; Editing by Toby Davis and Clare Fallon)
