The ban will start from the July transfer window this year and finish with the January transfer market in 2017 meaning newly appointed Real coach Zinedine Zidane will be unable to strengthen his squad this summer.
Atletico were also fined 900,000 Swiss francs (820,000 euros) and Real 360,000 (330,000 euros). However, both clubs are still allowed to sign players until the end of the month.
"The two clubs were found to have violated several provisions concerning the international transfer and first registration of minor players as well as other relevant provisions with regard to the registration and participation of certain players in competitions," said a FIFA statement.
"We will appeal, we think we are right and I think this is unjust," said Atletico president Enrique Cerezo.
"Not being able to sign is a problem because the seasons are very long and you always need players. Fortunately, we have a good and big squad with young players that can overcome these two windows without signings."
European champions Barcelona have just completed a one year ban for similar reasons.
Barca were initially banned in April 2014, but managed to delay the sanction taking effect until the transfer windows in January and the summer of 2015 by launching an ultimately unsuccessful appeal to the Court of Arbitration for Sport (CAS).
- Concerns flagged up -
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FIFA said the alarm was raised over the two clubs by FIFA's Transfer Matching System and its disciplinary committee completed the inquiry.
Under international football rules, players under 18 cannot be transferred to another country, except in limited circumstances. All transfers need the approval of a special FIFA committee.
The news is the latest off-field blow for Real having sacked two Champions League winning coaches in Carlo Ancelotti and Rafael Benitez in the past seven months, as well as being thrown out of the Copa del Rey for fielding an ineligible player.
The signing of Manchester United goalkeeper David de Gea was also frustrated at the last minute in August as the clubs failed to register the required paperwork in time.
La Liga leaders Atletico Madrid's usually hectic transfer policy will also be put on hold.
However, Diego Simeone's men look well-placed to cope with the ban having invested heavily in young talent over the past year.
Indeed, Atletico have already made two additions to their squad in January in Argentine international midfielders Matias Kranevitter and Augusto Fernandez.
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