Gary Hooper put the Hoops ahead on the half hour mark and two minutes from the finish Victor Wanyama doubled Celtics lead.
Hooper’s goal came after Scott Brown fired the ball into the box and it fell to Georgios Samaras, who slid it to Hooper and he tapped it home from close range.
There were calls for off-side but the linesman had already made his way back to the half-way line and the Celtic fans erupted into celebration. The party was well underway in Paradise.
A corner taken by Kris Commons in the 88th minute saw Victor Wanyama rise up inside the box and head the ball past the Helsinborgs keeper to make it 2-0.
Neil Lennon was delighted with the fact that Celtic were now taking their place with the most elite in European football saying this was the highlight of his career.
"It's the best thing I've done in football," the Hoops boss said.
"The pressure going into this game and, in particular the last five or six weeks, has been enormous.”
"I actually feel British clubs going into these games are at an unfair disadvantage because they're starting their season, so it makes the effort of the players and the performances even more remarkable in the circumstances."
Lennon recognised what this means to the fans and Celtic Football Club, who in their 125 year history were the first British Club to win the European Cup..
"You know what it means to the fans here and the club.
It's been four years in the waiting and I'm just so happy and so proud of them."
Hooper said it was quite an achievement for them to qualify for the group stages without a loss.
"It's very special. We've been waiting for it for four years. To play like that away and at home is amazing. To keep a clean sheet is a bonus and we're through to the group stage.
About the goal that caused the controversy he said: "I always look to see if I'm offside... I nearly missed it as well, but it just went in and I'll take it!"
Victor Wanyama spoke of his delight at getting the chance to play for Celtic against the other top teams in Europe.
"Celtic is a big club and I came here for the Champions League," he said.
"We've been working very hard and I'm very happy to get the chance to play in the Champions League”
He also paid tribute to the faithful Celtic support.
"The fans were keeping us going. They were fantastic today. They were with us from the beginning until the end and we are very proud of them."
"The teams which play in the group stages are all very good teams," he said. "We are looking forward to playing very, very big teams. We are very happy to make the group stages," he added.
Celtic will find out who they will face in the group stages in Thursdays draw.