The 41-year-old trainer takes over from Gregorio Manzano, who was officially relieved of his duties on Thursday less than six months after his arrival.
Simeone, who played for Atletico across two different spells between 1994-1997 and 2003-2005, joins the Spanish capital club after resigning from Racing Club.
The former defensive midfielder has signed a contract, which will keep him in charge of the Mattress Makers until the summer of 2013.
The coach has been handed the task of turning Atletico's fortunes around as the club currently sit 10th in the La Liga standings, 21 points off the top of the table.
The Mattress Makers are through to the Europa League Round of 32, where they are set to meet Lazio, but have crashed out of the Copa del Rey, following Wednesday's 0-1 defeat to Albacete.
Simeone began his coaching career in 2006, and has plied his trade with River Plate, Estudiantes and Catania among other clubs.
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