Leading 2-0 from the previous leg in Belfast, the Hoops recorded a comfortable 4-0 win at Parkhead to set up a showdown with Rosenborg in the next phase.
Scott Sinclair gave Celtic the lead on the night with just four minutes on the clock, driving home the rebound after debutant Olivier Ntcham's initial shot was parried by Linfield goalkeeper Roy Carroll.
Celtic's inevitable second came early in the second half when Rogic was given too much time and space on the edge of the area, the Australian letting fly and finding the bottom corner.
Seven minutes later, it was 3-0 to the home side as Sinclair helped himself to his second, latching on to a through-pass inside the box and curling a shot into the top corner.
The Englishman was Celtic's standout player throughout and he almost completed his hat-trick in the 64th minute, letting fly from the edge of the box with a dipping effort which Carroll tipped against the crossbar.
More relentless Hoops pressure ensued, with Linfield's only chance of note coming late on when defender Mark Stafford went for goal with an overhead kick, his effort dropping just wide of Craig Gordon's far post.
The hosts had to wait until stoppage time for number four as Rogic powered into the box with 92 minutes on the clock and lined up substitute Stuart Armstrong in front of goal, his teammate firing into the roof of the net.
Celtic will face Rosenborg in qualifying round three after the Norwegians edged past Dundalk of Ireland 3-2 on aggregate after extra time.