Media playback is not supported on this device
Leigh Griffiths and Stuart Armstrong secured a 34th win of the campaign for Brendan Rodgers' side, who were then presented with the Premiership trophy.
The feat was last achieved by Rangers in 1898-99, over an 18-game season.
And Celtic join Arsenal (2003-04) and Juventus (2011-12) in being unbeaten over a 38-game league season.
Rodgers' side, who won the League Cup in November, will attempt to win the club's first domestic treble since 2001 when they take on Aberdeen in Saturday's Scottish Cup final.
Celtic, who have won six top-flight titles in a row, are unbeaten in 46 domestic games this season (38 in league, eight in cups), and 47 domestic matches overall including the final league game of last season.
And they are unbeaten in 31 games in all competitions since losing to Barcelona in the Champions League on 23 November.
With the win and goals against Hearts, Celtic set new records for the Scottish Premier League/Premiership era, including goals, points, wins and margin of victory.
With so much anticipated from the hosts, Hearts head coach Ian Cathro sought to frustrate Celtic, restricting them to long-range efforts.
Kieran Tierney and Callum McGregor came closest with those and Griffiths sent a free-kick into the side netting.
And it could have been Hearts that went in front, Bjorn Johnsen laying a free-kick off for Alexandros Tziolis to strike narrowly over.
When Celtic did get into the box, goalkeeper Viktor Noring was in fine form.
The Swedish stopper made an instinctive block to deny Dedryck Boyata at a corner and then punched away Patrick Roberts' dangerous cut-back.
However, Hearts' resistance was broken when Roberts danced clear on the right and set up Griffiths for a confident header.
And Griffiths was involved in the second, his cross not properly cleared and falling for Armstrong to finish.
Though sustaining a fourth straight defeat, Hearts competed well in Glasgow and fared much better than their 5-0 home loss to Celtic last month - the match that clinched the title for Rodgers' men.
Johnsen headed against the right-hand post from a Malaury Martin corner as Cathro's men sought consolation.
And substitute Martin's volley was then kept out by Craig Gordon late on.
Match ends, Celtic 2, Heart of Midlothian 0.
Second Half ends, Celtic 2, Heart of Midlothian 0.
Tomas Rogic (Celtic) wins a free kick in the attacking half.
Foul by Jamie Walker (Heart of Midlothian).
(Celtic) wins a free kick in the attacking half.
Foul by Don Cowie (Heart of Midlothian).
Corner,  Heart of Midlothian. Conceded by Craig Gordon.
Attempt saved. Malaury Martin (Heart of Midlothian) left footed shot from the left side of the box is saved in the bottom left corner.
Corner,  Heart of Midlothian. Conceded by Erik Sviatchenko.
Corner,  Heart of Midlothian. Conceded by Kieran Tierney.
Krystian Nowak (Heart of Midlothian) hits the right post with a header from the centre of the box.
Corner,  Heart of Midlothian. Conceded by Scott Brown.
Attempt blocked. Malaury Martin (Heart of Midlothian) left footed shot from the left side of the box is blocked.
Callum McGregor (Celtic) wins a free kick in the defensive half.
Foul by Arnaud Sutchuin-Djoum (Heart of Midlothian).
Kieran Tierney (Celtic) wins a free kick on the left wing.
Foul by Euan Henderson (Heart of Midlothian).
Foul by Kolo Touré (Celtic).
Euan Henderson (Heart of Midlothian) wins a free kick in the attacking half.
Attempt missed. Dedryck Boyata (Celtic) header from the centre of the box is close, but misses to the left.
Corner,  Celtic. Conceded by Aaron Hughes.
Substitution, Celtic. Erik Sviatchenko replaces Stuart Armstrong.
Substitution, Heart of Midlothian. Euan Henderson replaces Alexandros Tziolis.
Goal!  Celtic 2, Heart of Midlothian 0. Stuart Armstrong (Celtic) left footed shot from the centre of the box to the top right corner.
Substitution, Celtic. Kolo Touré replaces Jozo Simunovic.
Foul by Patrick Roberts (Celtic).
Alexandros Tziolis (Heart of Midlothian) wins a free kick in the attacking half.
Attempt saved. Jozo Simunovic (Celtic) left footed shot from outside the box is saved in the centre of the goal.
Attempt missed. Leigh Griffiths (Celtic) left footed shot from outside the box is close, but misses to the right.
Attempt missed. Stuart Armstrong (Celtic) right footed shot from long range on the right is close, but misses to the left.
Substitution, Heart of Midlothian. Jamie Walker replaces Prince Buaben.
Attempt saved. Bjorn Johnsen (Heart of Midlothian) right footed shot from the left side of the box is saved in the centre of the goal.
Foul by Scott Brown (Celtic).
Arnaud Sutchuin-Djoum (Heart of Midlothian) wins a free kick in the defensive half.
Attempt missed. Patrick Roberts (Celtic) left footed shot from long range on the right is close, but misses to the left.
Foul by Dedryck Boyata (Celtic).
Malaury Martin (Heart of Midlothian) wins a free kick in the defensive half.
Attempt blocked. Scott Brown (Celtic) right footed shot from the right side of the box is blocked.
Attempt blocked. Tomas Rogic (Celtic) right footed shot from the centre of the box is blocked.
Attempt missed. Leigh Griffiths (Celtic) right footed shot from the right side of the six yard box is close, but misses to the right.
Champions Celtic beat Hearts to become the first team to complete a Scottish top-flight season unbeaten for 118 years.