The Turkish side were initially banned by UEFA from participating after allegations of match-fixing in their 2011 Turkish Cup final win over Buyuksehir Belediyespor.
They were temporarily reinstated while their appeal was heard by the Court of Arbitration for Sport (CAS), but the Swiss-based body has now confirmed Besiktas will not compete in the second-tier continental competition this season.
A CAS statement read: "CAS has today dismissed the appeal filed by Besiktas JK against the decision taken by UEFA to exclude it from the European Europa League 2013-14.
"Due to the urgency of the matter, the CAS Panel has issued its decision without the grounds. The full, reasoned award will be issued as soon as possible."
Besiktas battled back from a 2-1 first-leg deficit in their play-off with Tromso on Thursday night, winning the return 2-0 to secure a 3-2 aggregate triumph.
However, it will be Tromso who advance after UEFA's emergency panel held a meeting on Friday morning at which it decided the Norwegian team should be included in the draw for the group stage.
Another side to be granted a second crack at the Europa League were Cypriots APOEL, who were pulled out of the 'lucky losers' draw in Monaco on Friday morning.
The draw was necessary after CAS dismissed Fenerbahce's appeal against their exclusion, also for match-fixing after a widespread investigation which rocked Turkish football.
Fener would have dropped into the Europa League after losing their Champions League play-off with Arsenal, but APOEL, who lost their two-legged tie 3-2 to Zulte Waregem, will take part instead.
There is still one place in lunchtime's draw to be determined with the tie between AZ Alkmaar and Atromitos yet to be completed.
The second leg was abandoned after 59 minutes on Thursday night due to an electrical fire linked to the floodlighting system at the AZ Stadion.
When the game was stopped, AZ trailed 1-0 on the night but led 3-2 on aggregate. The match resumes on Friday morning.
Tottenham will be among the top seeds when the draw does take place.
Andre Villas-Boas' side will be guaranteed of avoiding Spanish sides Valencia and Seville, as well as French club Lyon.
Wigan and Swansea are both expected to be among the pot of third seeds.
The top two in each group will go into a knockout round of 32 clubs including the eight sides that finish third in the Champions League groups.