Brendan Rodgers’ side hosts the Eliteserien outfit at Parkhead on Wednesday, before travelling to Trondheim for the return leg next week.
The Hoops, who progressed to the draw after a 6-0 aggregate win over Alashkert of Armenia, could have faced a rematch against old foes Hapoel Beer-Sheva of Israel, Swedish side Malmo - who knocked Celtic out in Champions League play-offs in August 2015 - or HJK Helsinki.
Dinamo Zagreb, BATE Borisov, FK Suduva, Red Star Belgrade, Sheriff Tiraspol and Shkendija were also among the potential opponents. If Celtic lose to Rosenborg, they will face Cork City in the Europa League Third Qualifying Round.
Athens, who won the Greek Super League last year, haven’t qualified for the Champions League group stages in over a decade, when they defeated Hearts en route.
The Greeks competed in last year’s Europa League after defeating Club Brugge in the play-off round. Athens had dropped into the Europa League after losing to CSKA Moscow in the Champions League Third Qualifying Round.
They finished second behind AC Milan in the group stages, but were knocked out on away goals by Dynamo Kyiv in the round of 32.
Athens are no strangers to Scottish opponents, having faced Dundee United, Hearts, Hibs and Rangers in European competition.
AEK have lost just once to a team from Scotland in Europe - a 3-2 defeat to Hibs at Easter Road after extra time in September 2001 - and have recorded six wins and one draw.
The third round ties will take place on August 7 and 8 and August 14 and 15.