Both clubs were prevented from taking up their place in UEFA tournaments this season, as a result of historical match-fixing allegations.
An official UEFA statement read: "The UEFA Appeals Body today announced its decisions following the appeals lodged by Besiktas JK and Fenerbahce SK related to the two decisions passed by the UEFA Control and Disciplinary Body (CDB) on 21 and 22 June 2013, respectively.
"The UEFA Appeals Body carefully analysed the statements and documents submitted by Besiktas JK and Fenerbahce SK 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 JK has had their appeal rejected. Consequently, Besiktas JK is not eligible to participate in the 2013-14 UEFA Europa League. Fenerbahce SK has had their appeal partially admitted. Consequently, Fenerbahce SK is excluded from participating in the next two UEFA club competitions for which they would qualify, including the 2013-14 UEFA Champions League."
Both clubs still have the option to take a further appeal to the Court of Arbitration for Sport, but face a race against time to have their cases heard in time to play on the continent next season.