The ruling means that last season's Turkish League runners-up Trabzonspor, who were re-instated as Fenerbahçe's replacements after earlier losing in the third qualifying round to Benfica, will remain in the competition.
Their first match is against 2010 European champions Inter Milan on Wednesday.
More than 30 players and officials have been jailed pending trial, including Fenerbahçe chairman Aziz Yıldırım, over alleged manipulation in 19 matches.
"The Court of Arbitration for Sport has dismissed an urgent request for provisional measures filed by Fenerbahçe SK following a decision of the Turkish Football Federation to withdraw the club from the UEFA Champions League," CAS said.
The statement on its website said Fenerbahçe had requested to be allowed to participate in the Champions League group stage which starts next week.
The Turkish football federation (TFF) has said it would not take any decisions regarding individuals or clubs involved in alleged match-fixing until a Turkish court accepts the indictment and ends a ban on the disclosure of evidence. That could take several months.
However under pressure from UEFA, the TFF then excluded Fenerbahçe from the Champions League, allowing Trabzonspor to take their place.
The TFF has postponed the start of the season by a month until this weekend.