The ban will start from the July transfer window this year and finish with the January transfer market in 2017.
Atletico were also fined 900,000 Swiss francs (820,000 euros) and Real 360,000 (330,000 euros).
“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.
Barcelona has just ended a one year ban for similar reasons.
