Neil Lennon’s men earned a 1-0 aggregate victory thanks to Kris Commons’ goal in last week’s first leg as they edged past their spirited opponents.
The draw for the play-off takes place on Friday, with the Parkhead club a step closer to the lucrative group stages of the competition from which they emerged last season to reach the last 16 of the competition.
On the Swedish club’s artificial surface, both teams had chances in an opening 45 minutes with Elfsborg’s on-loan striker, Mo Bangura, firing a spectacular overhead effort just past Fraser Forster’s left-hand post.
Bangura had another opportunity in the 28th minute when, after slipping away from Celtic defender Efe Ambrose easily enough, his header from 10 yards lacked conviction as it looped over the bar.
Between those chances, however, the Scottish champions could have twice taken the lead and probably killed off the home side.
In the 12th minute Georgios Samaras spurned a great chance soon when Swedish right-back Mikael Lustig reached the byline before standing up a delightful cross for the unmarked Greek striker but he headed high over the bar from 10 yards.
In the 20th minute Celtic had another opportunity when Elfsborg defender Jon Jonsson clumsily handled the ball 25 yards from goal, preventing Samaras getting through.
Commons’ driven free-kick broke off the defensive wall to Joe Ledley who shot straight at goalkeeper Kevin Stuhr-Ellegaard, albeit the Wales midfielder appeared to have his jersey tugged before he got his shot away.
Five minutes after the restart Elfsborg defender Johan Larsson tried his luck from distance after receiving a corner but his effort went well wide of the target.
There was a moment of a panic inside the Hoops box in the 55th minute from Larsson’s long throw, with the ball coming off the post in the melee, but the assistant referee had his flag up to indicate an infringement.
There appeared to be a decent Elfsborg penalty claim five minutes later when Wilson tackled fellow Englishman James Keene inside the box but Russian referee Vladislav Bezborodov was not impressed.
As the match entered its final stages the Swedes became increasingly desperate but the Hoops defence restricted them to very few chances and saw the match out with a degree of comfort and indeed with more poise they might have made more of several counter-attacks.