The bans do not cover the current transfer window, which runs until the end of this month.
“The FIFA appeals committee has conceded a provisional suspension while our appeal is presented,” Atletico wrote on their Twitter account.
Real added on their website (www.realmadrid.com): "Real Madrid has announced that the FIFA Appeal Committee has decided to provisionally suspend the sanction imposed on the club."
Both clubs announced they would appeal after being given the punishments earlier this month.
The FIFA probe concerned players featuring in competitions with Atletico from 2007 to 2014 and with Real from 2005 to 2014.
La Liga leaders Barcelona were handed a similar penalty in April 2014 for breaching the same regulations that prevent the registration of minors in any country other than their own, except in specific circumstances.
Barca were allowed to sign players during the following close season with the ban becoming effective at the start of 2015 following the rejection of their appeal.
Barcelona signed Arda Turan and Aleix Vidal ahead of this season from Atletico Madrid and Sevilla respectively but the pair had to watch from the sidelines due to the FIFA ban.
They were eligible to play from the start of this year.
(Reporting by Tim Hanlon in Barcelona, editing by Ken Ferris)
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