The 32-year-old's contract was due to expire this summer but they have decided to part ways early.
Arca has been dogged by a toe injury this season which has limited him to just one league appearance, and he has not played at all in 2013.
Arca joined Boro from local rivals Sunderland in 2006 and made over 150 appearances during his time on Teesside.
A Boro spokesman told the Evening Gazette: "We've cancelled Julio's contract, which is due to expire this summer, by mutual consent to enable him to return to Argentina to further his rehabilitation."
Boro boss Tony Mowbray added: "We'd like to thank Julio for all his years of service and we wish him well."