The court says it upheld an appeal by rider Alexander Peternell that he should have been selected instead of the only other candidate, Paul Hart, who was chosen by South Africa's equestrian federation and Olympic committee.
Peternell is ranked 164th in the world and Hart is No. 442.
CAS says its panel found that Peternell "fulfilled the three different sets of selection criteria applicable and accordingly, that he should have been nominated."
The eventing competition, comprising dressage, cross-country and jumping rounds, begins Saturday and ends Tuesday.