Karlssons appealed last year that the International Equestrian Federation (FEI) subsequently decided to delete ranking points earned in three competitions in France, among other things due to too small starting fields.
The decision affected Karlsson, who had earned many points in those competitions, and she lost her Olympic place.
Only on Tuesday did the decision in Cas become official, writes DN.
"The decision is a disappointment to the FEI, but we respect it because we know that mistakes have been made and that Cas based its decision on those mistakes," said FEI Secretary-General Sabrina Ibáñez in a press release.
Karlsson, 35, was born in Sri Lanka and was adopted by a Swedish family when she was an infant. She has lived in Germany for a long time, but competed for Sweden until 2018.