"For its midfield, AC Milan was looking for an experienced, professional player with the will to do well," Milan said in a statement (www.acmilan.com).
"The club has found these three elements in you," they said of the skilled former Argentina midfielder nicknamed El Principito (little prince) in his homeland.
The 31-year-old player joined Besiktas, initially on loan, in 2014 from Ukrainian club Metalist Kharkiv. He made 31 league appearances and scored seven goals last season.
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Before joining Besiktas, Sosa had a six-month spell on loan at Atletico Madrid, during which he helped the Spanish club win the 2013-14 league title.
Sosa, who began his career at Estudiantes and has also played for Bayern Munich, has previous experience in Serie A, having had a one-year stint at Napoli in 2010-11.
"Thank you Sosa for your efforts, we wish you success in your future career," the Istanbul-based club said on their website (www.bjk.com.tr).
Sosa had been seeking a move from Turkey since the bomb attacks on Istanbul airport early last month, fearing for the security of his family, according to Argentine media reports at the time.
AC Milan, who missed out on Europe for the third consecutive season after finishing seventh in the 2015-16 campaign, begin their season at home to Torino on Sunday.
($1 = 0.8878 euros)
(Reporting by Silvia Recchimuzzi in Gdynia,; Editing by Neville Dalton/Rex Gowar)
