Spanish side had originally been barred from signing players for two windows by world governing body FIFA.
They remain banned from registering new players this January but will now be able to make signings next summer.
The club have also had their fine reduced from 360,000 Swiss francs (£282,000) to Sfr 240,000 (£188,000).
Both Real and fellow Spanish side Atletico Madrid were banned after breaching rules over the transfer of foreign players under the age of 18.
In a statement on their official website, Real said: “The decision highlights the injustice of the original ban imposed by FIFA, although the club regrets that CAS lacked the courage to revoke the ruling entirely.’’
No information has been given regarding Atletico’s appeal against their ban and fine.
FIFA initially ruled on the case in January, but the appeals meant both Real and Atletico could sign players last summer.
The world governing body’s investigation concerned players aged under 18 who played in competitions for Atletico between 2007 and 2014, and Real from 2005 to 2014.
FIFA bans the transfer of under-18s to different countries unless they meet strict criteria.
It brought in the rules to help protect children from exploitation and trafficking.
Now, under-18s can only be transferred abroad if the player’s parents move to the country in which the new club is located for non-footballing reasons
It can also be possible if both clubs are in the European Union (EU) or European Economic Area (EEA) and the player is aged between 16 and 18.
However, in this case, the buying club must meet more criteria relating to education, training, living conditions and support.
Last year FIFA dealt with more than 2,700 applications for the transfer of a child to a club in another country, with almost 400 of those applications rejected.