Gary Hooper and Victor Wanyama were on target in either half as the Glasgow outfit reached the group stages for the first time since the 2008/09 season.
Neil Lennon's men took a 2-0 lead into the second leg of their play-off against the Swedish side and Hooper's close-range strike on the half-hour mark, albeit from what looked like an offside position, effectively ended the contest.
Two minutes from time Wanyama headed in a Kris Commons cross to put gloss on a fine victory and confirm the Hoops' place in Thursday's draw in Monaco.
Celtic will face tougher challenges ahead but the boost from the club's participation in European football's elite club competition, both in terms of finance and morale, and in lifting the profile of the game in Scotland, cannot be underestimated.
Lennon welcomed four key players back into his starting line-up.
Skipper Scott Brown, wide-man Georgios Samaras and midfielder Commons had missed the 4-2 win at Inverness in the Clydesdale Bank Premier League on Saturday through injury but were reinstated along with winger James Forrest, who was rested in the Highlands.
There was a late change to the Swedish champions' team sheet with 19-year-old defender Joseph Baffo replacing Loret Sadiku, who was not even on the bench.
The early stages were mostly uninspiring.
Helsingborg manager Age Hareide had claimed one goal for his side would envelop Celtic Park in nerves and when the visitors did approach the home side's penalty area there were audible signs of apprehension.
Celtic left-back Emilio Izaguirre was robbed by Alejandro Bedoya in the 15th minute, leaving the Parkhead defence exposed but the former Rangers player fluffed his shot from the edge of the box.
The anxious Hoops fans raised the decibel levels whenever their side ventured forward, notably in the 20th minute when Samaras, who had an inspirational first half, burst into the Helsingborg box after leaving Erik Wahlstedt and Ardian Gashi in his wake, only to send a tame shot into the arms of Par Hansson.
There was a vociferous claim for a Celtic penalty five minutes later when Baffo ended Forrest's mazy run with a challenge inside the Helsingborg box but while referee Carlos Carballo stood firm, the visitors were wilting.
Moments later Hansson had to stretch to ensure Samaras' cross did not creep under the bar but penalty-box poacher Hooper struck from the resultant corner.
Commons played a short pass to Forrest whose driven cross from the bye-line was cleared only to Brown outside the box.
When the Scotland midfielder's mis-hit shot arrived at Samaras, he casually helped the ball on to the former Scunthorpe striker, who knocked in from close range and allowed others to debate a possible offside.
Helsingborg's chances instantly evaporated along with the home fans' nerves and the Celtic supporters sang their favourites along to the half-time whistle.
Five minutes into the second half Hoops keeper Fraser Forster, who made several crucial saves in the first leg, had to dive to his left to push a curling 25-yard free-kick from Jere Uronen round the post, with the home side surviving the corner.
Helsingborg striker Nikola Djurdic then hit the side netting with an attempt following another corner moments later, before Forster was tested again from distance, this time by midfielder May Mahlangu but the former Newcastle keeper gathered at the second attempt.
David Accam replaced Thomas Sorum for the visitors just after the hour mark and picked up a booking moments later for a foul on Izaguirre.
Most of the sting, however, had left the game.
In the 70th minute Samaras enjoyed a deserved cheer and round of applause from the home supporters when he was replaced by Tony Watt, who had notched two at Inverness at the weekend.
It was testament to Celtic's control that this was a substitution made to give the youngster European experience, as opposed to asking him to rescue the game.
Watt had a chance 10 minutes from time when the ball bounced around the Helsingborg box but his header was too weak to worry Hansson.
Moments later Forrest crashed a left-footed drive from 20 yards off the post with Hooper this time flagged offside when the rebound landed at his feet.
As the game stretched further in the closing stages, Bedoya twice threatened the Hoops goal and Hansson made saves from Brown and Watt before Wanyama headed in Commons cross with two minutes remaining.
There was time for Forrest to blaze over the bar in a Celtic break but, by that time, Lennon and the Celtic fans were thinking ahead to Thursday's draw and which three clubs will be visiting the east end of Glasgow in the next stage of the tournament.