The sanction means the clubs, currently third and first respectively in Spain's top division, will not be able to register new signings until July 2017 once the present transfer window closes at the end of the month.
Real, the world's richest club by income, denied wrongdoing and confirmed they would appeal, while Atletico president Enrique Cerezo told Spanish radio station Cadena Ser that they would also contest the verdict.
"It's a great injustice and not being able to sign players is a problem but our squad is sufficient," he said.
Real's great rivals Barcelona, standing second in La Liga, were handed a similar penalty in April 2014 for breaking the same set of regulations.
However, Barca's ban was not announced during a transfer window, meaning they were unable to make quick adjustments to their squad as Real and Atletico can over the next two and a half weeks.
Real, with new coach Zinedine Zidane just over a week into the job, are unlikely to offload players but could use their considerable financial muscle to bolster their ranks.
At Atletico, forwards Fernando Torres and Jackson Martinez could leave and be replaced having failed to settle into the team this season.
Barcelona took their appeal to CAS, where it was rejected, and the ban eventually finished with the start of the current window, which runs until the end of January.
The Spanish and European champions bought Arda Turan from Atletico and Aleix Vidal from Sevilla in July but they were unable to play until the turn of the year, although still allowed to train with their new team mates.
SPECIFIC CIRCUMSTANCES
FIFA says its rules are designed to protect minors who move to other countries and prevent soccer clubs from exploiting them.
It notes that the need for the strict application of these rules has been "confirmed on various occasions" by the Court of Arbitration for Sport (CAS).
"Opening up the door to exceptions beyond those carefully drafted and included in the regulations would unavoidably lead to cases of circumvention of the rationale for these provisions," FIFA said on Thursday.
Atletico were fined 900,000 Swiss francs (624,501 pounds) and record 10-times European champions Real 360,000 francs, they added.
The two clubs were given 90 days to regularise their situation but can continue to sell players during the ban.
FIFA said that "the two clubs were found to have violated several provisions concerning the international transfer and first registration of minor players."
The probe concerned players who participated in competitions with the clubs between 2007 and 2014 in the case of Atletico, and between 2005 and 2014 in the case of Real Madrid.
"FIFA works hard to protect the rights of players under the age of 18 -- whether male or female, amateur or professional," it said in a statement.
"This is done through the enforcement of regulations prohibiting the international transfer of minors, or the first registration of minors in a country other than their own, except in specific circumstances."
The next two transfer windows are July/August 2016 and January 2017.
($1 = 1.0040 Swiss francs)
(Additional reporting by Iain Rogers; writing by Brian Homewood in Zurich; editing by John Stonestreet, Justin Palmer and Toby Davis)
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