Both bans were linked to a domestic match-fixing scandal which rocked Turkish football in 2011.
The two clubs asked UEFA in June to re-examine their punishments and in both cases European soccer's governing body decided to uphold the sanctions.
It said in a statement: "The UEFA Appeals Body carefully analysed the statements and documents submitted by Besiktas and Fenerbahce related to their specific cases, as well as the statements and documents submitted by the UEFA Disciplinary Inspectors appointed to each case, and reached the following decisions.
"Besiktas have had their appeal rejected. Consequently, Besiktas are not eligible to participate in the 2013/14 UEFA Europa League.
"Fenerbahce have had their appeal partially admitted. Consequently, Fenerbahce are excluded from participating in the next two UEFA club competitions they qualify for, including the 2013/14 UEFA Champions League."
The clubs have the right to appeal against the decisions at Court of Arbitration for Sport (CAS).
(Reporting by Toby Davis in London; editing by Ken Ferris)
