The defending champions dominated from start to finish against the Edinburgh-based side, but it took until 29 minutes for Leigh Griffiths to put the home team into the lead.
Read below to see how the action unfolded in Glasgow.
12.01pmHello, and welcome to Sports Mole's live coverage of the match in the Scottish Premiership between Celtic and Hearts.
12.03pmCeltic had little to no competition as they stormed to the Scottish Premiership title without losing a game last season, but there is always excitement ahead of the new campaign and their fans have been counting down the days until they get an opportunity to try to replicate their record-breaking year. The could have been handed an easier start than a meeting with Hearts, but it represents a chance for the Glasgow giants to set their stall out in this league opener.
12.06pmAs for Hearts, they are not a club in disarray but they are not far from it. Earlier this week, boss Ian Cathro left the club and it has led to Jon Daly being placed in temporary charge. It has not been the ideal preparation for the Edinburgh-based side but it leaves them making the short trip east with little to lose. Seven new signings have been made during the summer and the players selected for this afternoon's contest will be eager to make an impression on Scottish football's biggest stage.
12.07pmWithout further ado, let's take a look at the team news coming from Celtic Park, starting with the defending champions.
12.09pmCELTIC XI: Gordon, Lustig, Bitton, Simunovic, Tierney, Brown, Ntcham, Forrest, McGregor, Sinclair, Griffiths
12.10pmCELTIC SUBSTITUTES: De Vries, Armstrong, Hayes, Rogic, Ajer, Ralston, Kouassi
12.11pmHEARTS XI: Hamilton, Brandon, Berra, Hughes, Grzelak, M.Smith, Buaben, Cowie, Djoum, Moore, Lafferty
12.12pmHEARTS SUBSTITUTES: Noring, Souttar, Nowak, Randall, Martin, Sammon, Isma
12.16pmAs expected, Celtic boss Brendan Rodgers names his strongest side with both Scott Sinclair and Leigh Griffiths getting the nod in attack. New signing Olivier Ntcham features in midfield alongside Scott Brown, while Nir Bitton drops back to the centre of defence after an injury to Erik Sviatchenko. Winger Jonny Hayes - who has joined from Aberdeen - has to settle for a place on the bench.
12.19pmAs for Hearts, four of their new signings are given a role in the starting lineup, with Christophe Berra, Rafal Grzelak, Michael Smith and Kyle Lafferty all featuring in the side. Liverpool loanee Connor Randal must make do with a spot among the replacements.
12.22pmPREDICTION! Celtic are the clear favourites to win this match and we can find no reason to go against that. It has less than 72 hours since they beat Rosenborg in Norway but backed by a sold-out home crowd, they should be able to claim a relatively simple win. Rodgers's team to win 3-0.
12.25pmIt's time for the two teams to make their way out to the warmest of receptions from both sets of supporters. I think they are pleased that Scottish Premiership football is back!
1 minHearts get us underway at Celtic Park.
3 minIt's been a solid start from Hearts, who have spent the majority of the opening minutes in the Celtic half, but the home side came close to creating the first chance, only to see a cross cleared.
4 minCHANCE! What on earth are the Hearts defenders doing here? A corner from Griffiths finds Bitton all on his own at the back post, but the stand-in defender heads into the side-netting from eight yards.
8 minDaly would have been encouraged by his side's start to this game, but they now find themselves under constant pressure from the home side. There have been no more opportunities but already, it only feels a matter of time for Celtic.
11 minNtcham looks a quality addition in the centre of midfield for Celtic. He has already made a few nice touches and sprayed a pass forward which created a crossing opportunity on the left.
12 minSHOT! Better from Hearts who create a shooting chance for Buaben from outside of the area but his attempted curler is miscued and Gordon is able to make the easy save.
16 minThe pace of the game has slowed down a touch and that probably suits Hearts. Celtic are still having the majority of possession but they are given Hearts longer to set themselves in the final third.
20 minCeltic must have heard me because they have stepped things up again now. There's a certain amount of panic in the Hearts defence when they are faced with the speed of Sinclair and Griffiths and it is something which Celtic should look to use to their advantage. Still no more attempts on goal.
23 minCHANCE! This is excellent determination from Griffiths, who rides a couple of tackles before finding himself in a shooting position inside the penalty area. However, his effort is straight at Hamilton, who manages to punch the ball clear, before a defender makes a last-ditch challenge to prevent the rebound being converted.
25 minCHANCE! Celtic are dominating now. Sinclair slides the ball through to Griffiths but he slices his shot from around 14 yards wide of the near post.
27 minBOOKING! Brown is no stranger to yellow cards and he goes into the book for a late challenge on Djoum.
29 minGOAL! Celtic 1-0 Hearts (Griffiths)
29 minThis is probably the first of many goals for Griffiths this season. A long ball finds the run of the Scottish striker and after biding his time to hold off challenges from Hamilton and Grzelak, he slotted home from close range. Celtic take the lead at a time when Hearts had just began to make an impression at the other end.
30 minBOOKING! Lafferty has been running a tightrope since the start of the game and it is no surprise that he goes into the book. I'm not sure if it was for a foul or his protests but either way, it was deserved.
34 minHearts are still showing glimmers of confidence in the final third but you would expect that one more goal will be enough for Celtic to run out comfortable winners. It's imperative that Hearts reach the break no more than 1-0 down.
35 minGriffiths is starting to run rings round Berra. He holds off the defender before cutting inside onto his left foot. His effort seems destined for the net, but a Hearts player gets in the way to deflect the ball over the crossbar.
39 minSHOT! I'm not sure how long Hearts can hold out. They are pressed into their own penalty area and only Hamilton is keeping the score down. On this occasion, Forrest finds some space before seeing a shot saved at the near post.
42 minSHOT! Griffiths is over a free kick around 25 yards from goal - a similar position to his second goal for Scotland against England - but he curls the ball well over the crossbar.
44 minBOOKING! Michael Smith goes into the book for a cynical pull of Griffiths's shirt.
45 minHALF TIME: Celtic 1-0 Hearts
1.16pmCeltic reach the break with their 1-0 lead still intact, but they came within inches of doubling their advantage as McGregor hit a shot wide of the far post after being played in by a clever flick from Brown. Hearts will be relieved to face just a narrow deficit heading into half time.
46 minCeltic get us back underway in Glasgow.
49 minHearts had to withstand some pressure from Celtic soon after the whistle but they have responded well. From a corner, Berra should be getting an effort on target after jumping above the defence but he failed to make enough contact with the ball.
51 minGOAL! Celtic 2-0 Hearts (Sinclair)
51 minThat might be that. Celtic are unfortunate not to score from a move which ended with Hamilton saving from McGregor but from the resulting corner, they double their advantage when Sinclair nets from close range after a miscued clearance from Hughes.
55 minDon't be surprised to see Rodgers ring the changes from here. Celtic only faced Rosenborg in Norway on Wednesday night and he will be keen to rest a few of his players. They are coasting now.
59 minSHOT! Celtic are playing with a sense of freedom which suggests that they know this game is wrapped up. A long passing exchange ends with McGregor being denied by a save by Hamilton, who got a strong hand behind the ball.
62 minSHOT! McGregor is desperate to get onto the scoresheet. He finds more space on the edge of the area before lashing an effort marginally wide of the post.
62 minSUBSTITUTION! Hearts make their first change, with Liverpool loanee Connor Randall coming on for Buaben.
63 minGOAL! Celtic 3-0 Hearts (Griffiths)
63 minCeltic net what was becoming inevitable third. Brown releases McGregor into the penalty area and his cutback is headed into the net from inside the six-yard box by Griffiths.
67 minSUBSTITUTIONS! There will be no hat-trick for Griffiths because he is being replaced by Jonny Hayes.
69 minBOOKING! Grzelak has got away with a couple of strong challenges already, but not this time. He is then substituted for Esmael Goncalves.
71 minSUBSTITUTION! This is a smart decision from Daly. He replaces the volatile Lafferty with Connor Salmon.
73 minGOAL! Celtic 4-0 Hearts (McGregor)
73 minCeltic are absolutely rampant. A surging run from Sinclair ends with a pass to McGregor, who only has one thought in his mind and lashes a swerving effort into the roof of the net from 20 yards.
75 minSUBSTITUTION! It's time for McGregor to make way, with Tom Rogic being introduced in his place.
81 minAll credit to Hearts, who continue to try to create something in the final third, but they remain unable to get a shot on goal which may test Gordon. Their former goalkeeper has had very little to do this afternoon.
84 minGOAL! Celtic 4-1 Hearts (Goncalves)
84 minIs the great escape on? Probably not, but Hearts net a consolation goal through Goncalves, who finds the roof of the net from an acute angle, via a deflection off Gordon.
87 minSUBSTITUTION! A final change for Celtic sees Stuart Armstrong come on for Ntcham.
90 minThere will be three minutes of added-on time.
90+3 minFULL TIME: Celtic 4-1 Hearts
2.22pmThe full-time whistle goes at Celtic Park and the home side have successfully saw out a 4-1 victory over Hearts. Leigh Griffiths was the pick of he players but each of Brendan Rodgers's team contributed to an easy win.
2.22pmThat will be all from Sports Mole for this match. Thank you for joining us this afternoon and we hope to see you again soon. Goodbye for now.