The 28-year-old, who has played for Bayern Munich and Napoli during his career, has spent the last three years at Metalist and was the Ukrainian club's captain, but he wanted to head back to Europe's major leagues in an attempt to make Argentina's World Cup squad.
He made seven appearances in his country's qualification for the 2014 tournament in Brazil but has not played in the Champions League this season and will boost Diego Simeone's squad for the round of 16 tie against Milan.
"FC Metalist captain Jose Sosa received permission from the club president Sergiy Kurchenko to go on six-month loan to one of the European clubs," a statement from Metalist read.
"We listened to Jose Sosa's request that he wants to win a place in the Argentina national team to participate at the World Cup in 2014, which will be held in Brazil.
"Given Jose's contribution to the development of the club and taking into account the fact that the championships in European countries are held during the winter, in contrast to Ukraine, we have decided to meet Sosa's wish to go on six-month loan to one of the European clubs."
Sosa will undergo a medical on Thursday.
Atletico went into the mid-season break level on points with table-toppers Barcelona and will resume their league campaign at Malaga on Saturday before facing the Catalan giants a week later.