The ruling means Nottingham Forest, who finished seventh in the Premier League last season, will take their place in the Europa League.
Palace qualified for the Europa League after winning last season's FA Cup final against Manchester City, but were punished by UEFA for breaching multi-ownership rules.
Businessman John Textor owns a share of Crystal Palace and is a majority shareholder in Ligue 1 side Lyon, who also qualified for the Europa League.
Last month the Eagles appealed to CAS against the ruling, Nottingham Forest and Lyon.
A statement from CAS read: "The Court of Arbitration for Sport (CAS) has dismissed an appeal by Crystal Palace FC (CPFC) against UEFA, Nottingham Forest FC and Olympique Lyonnais (OL) concerning a decision by UEFA to remove CPFC from the UEFA Europa League 2025/2026 due to a breach of UEFA multi club ownership regulations.
"As a result, CPFC will be admitted to compete in the UEFA Conference League 2025/2026."
As both Lyon and Palace had qualified for the Europa League, the French club were allowed to keep their place as they had finished higher in their respective league. Lyon finished sixth in Ligue 1 while Palace were 12th in the Premier League.
Palace, who won the Community Shield on Sunday beating Liverpool in a penalty shootout, are set to play in the Conference League's qualifying playoff round later this month.