A brace from Virgil van Dijk and another goal from Teemu Pukki inside the opening half-hour set up the win, before the latter completed the scoring just under 20 minutes from time to complete a 5-0 aggregate success.
The Hoops opened the scoring on 14 minutes when Stefan Magnusson was caught under a corner from Kris Commons and Van Dijk bundled the ball over the line from close-range after Charlie Mulgrew sent a header into the six-yard box.
Magnusson was culpable once again six minutes later as Mikael Lustig got on the end of another deep Commons corner to nod the ball back across goal and Van Dijk planted his header inside the post.
Pukki (27) put the match beyond the visitors when he stretched to turn the ball over the line from a low Callum McGregor delivery after Emilio Izaguirre opened up the Reykjavic defence with a sublime pass.
And the diminutive striker added the fourth when he touched the ball past the advancing goalkeeper and blasted his angled shot into the top corner on 71 minutes.
Celtic came close to opening the scoring after five minutes when Commons played a superb reverse pass to Pukki, but his effort was blocked by Magnusson before the keeper turned the rebound from Leigh Griffiths round the post.
Pukki later showed a great turn of pace before forcing Magnusson into the smart save just before he got on the scoresheet, and the Finland international flashed another effort narrowly wide in the latter stages of the first half.
Commons twice tested Magnusson in the early stages of the second half with two fierce shots which the keeper was equal to.
And when Commons did beat Magnusson with a drive seven minutes from the end, the midfielder was denied by the post.