The former Boca Juniors centre-back, 33, has spent the past five years with Getafe and won 12 international caps.
"He is a player with great personality and a tremendous winning character," sports director Jose Luiz Perez Caminero said in a statement.
"We expect to him to bring his knowledge and experience to the defence and to help his younger colleagues to develop."
Diaz becomes Atletico's third reinforcement after the arrivals of Uruguay forward Cristian Rodriguez and Turkey midfielder Emre Belozoglu.
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