Elsewhere, Ajax survived the dismissal of Joel Veltman to clinch a 4-3 aggregate win against Schalke, who won the second leg 3-2 after extra time at the VELTINS-Arena.
A statement released by Uefa read: "The CEDB has chose to exclude Olympique Lyonnais [and Besiktas] from participating in the next Uefa club competition for which it will qualify".
Lyon and Besiktas were handed suspended European bans and fined 100,000 euros each on Wednesday after crowd violence scarred their Europa League quarter-final match in France, UEFA said.
With a top-three finish in Ligue 1 no longer a prospect, the Europa League represents Lyon's only chance of a return to the Champions League, which could prove crucial in their ability to hold on to top scorer Alexandre Lacazette.
Matching each other penalty for penalty until number six, Dusko Tosic saw his effort saved by Lyon's Anthony Lopes but Christophe Jallet skied over the crossbar for Lyon. But Lopes saved again from Matej Mitrovic, allowing Gonalons to calmly convert and send Lyon through. However, Talisca grabbed his goal in the 58th minute, which ultimately sent the tie extra time and penalties.
As a precaution, Lyon advised fans not to travel and only a dozen Lyon fans made the journey to Istanbul, comfortably and safely seated in the VIP section as Besiktas fans happily snapped up their seat contingent.
Soon after the visitors were made to pay for that miss as Besiktas took the lead when Oguzhan Ozyakup received a quickly taken corner and fed Talisca, who turned and fired low through a crowd of players into the bottom-left of the goal.
Leandro Trossard replied four minutes later for the Belgian hosts but they were unable to find a victor.
It was Lacazette's 29th goal of the season, and moments later it looked as though he had taken his tally to 30, only for his sumptuous curling effort to rebound off the woodwork.
Besiktas will feel the absence of suspended striker Vincent Aboubakar but have an able deputy in Cenk Tosun.
Seven minutes later however, Lyon were in control once more.
Lyon nearly produced another swift riposte as Lacazette thumped an effort straight at Fabri when played through and the Besiktas keeper - at fault for Lyon's victor last week - produced a superb save after Lucas Tousart's shot deflected heavily off Atiba Hutchinson.
Just last December clashes broke out in a game between the Turkish side and Dinamo Kiev.