Fenerbahce will be declared winners by default while Besiktas will not be able to play in the Cup next season and will pay back the 4 million Turkish lira (£698,820) they earned from the competition this year.
"Besiktas made a difficult decision. I would have preferred to lose instead of winning this way," Fenerbahce coach Aykut Kocaman told reporters.
The April 19 second-leg game between the long-time Istanbul rivals had started in a tense atmosphere at Fenerbahce's ground and Besiktas were reduced to 10 men after former Real Madrid defender Pepe was sent off for a reckless tackle.
The teams were locked at 0-0 when the match was halted in the 57th minute after Besiktas coach Senol Gunes was struck by an object thrown from the stands. He needed five stitches in his head after he was taken to hospital.
The sides were level on aggregate at 2-2 after a tense first leg at Besiktas during which three players were sent off.
The Turkish Football Federation (TFF) ruled last week that the match should resume behind closed doors from the time when it was stopped. Fenerbahce were fined one million lira and their ground closed to supporters for three matches.
Besiktas reacted to the decision with "sorrow and regret" and tried to overturn it in court but their appeal was rejected on Wednesday.
Fenerbahce will play Akhisarspor in the Cup final.
(Reporting by Ece Toksabay and Tuvan Gumrukcu, editing by Ed Osmond)
