The Turkish giants had both been barred from competing in European competition next season but will be allowed to compete in the preliminary rounds pending a final decision
The decision means that Fenerbahce will enter the Champions League preliminary round in the upcoming 2013-14 season, having previously looked set to miss out on European football due to a 24-month continental ban for their part in the Turkish match-fixing and corruption scandal.
Besiktas were also set to lose out on playing in the Europa League this year due to a one-year ban but, following Thursday's decison by CAS, there is yet a chance that both sides could be cleared.
"Due to agreements reached between the appellants and Uefa, the decisions challenged by Fenerbahce and Besiktas have been stayed and will not be enforced until the CAS issues its final decision in each matter," a statement frm CAS read.
"This means that Fenerbahce SK and Besiktas JK will take part in the draws of the first preliminary matches of the Champions League (Fenerbahce) and of the Europa League (Besiktas).
"In the meantime, the arbitration procedures are continuing following an expedited calendar agreed upon by the parties and it is anticipated that hearings will take place in August with a final decision being issued before 28 August 2013 (Fenerbahce) and 30 August 2013 (Besiktas)."
Fenerbahce president Aziz Yildrim said the club intend the fight to prove that the ban is unfair on the club following the decision to suspend the ban temporarily.
"The Fenerbahce football team will participate in the Champions League this season," Yildirim told the club's official TV channel. "We'll move on, starting with Friday's draw. Enjoy this. I thank our lawyers here and vow that we'll fight until the end. The world and Turkey will see that Fenerbahce are right."
The decision means that the club, who reached the semi-finals of last season's Europa League, will be included in Friday's Champions League third qualifying round draw, although the final decision on their case could yet result in them being prohibited from participation in the group stage of the competition.
The Uefa ban had been met with a furious reaction in Turkey, with Fenerbahce's players understood to be preparing to lobby the European body over the severity of the penalty in light of them having already been imposed a previous competition ban in 2011-12 relating to the same scandal.
A final CAS decision for Fenerbahce's case will be taken on August 28, with Besiktas' fate set to be heard two days later.