Celtic beat Linfield 4-0 at Parkhead on Wednesday night to seal a 6-0 aggregate success against David Healy's side.
Scott Sinclair scored early on and Tom Rogic, Sinclair and Stuart Armstrong all struck after the break to complete an emphatic victory.
Brendan Rodgers' men now face Rosenborg in the third qualifying round of the Champions League, with the first leg at Celtic Park on Wednesday and the return in Norway a week later.
