The Italy international moved to San Siro on loan from Southampton in August, but has struggled to break into the first team.
Reports have also suggested Osvaldo has had bust-ups with team-mates at Inter and he has not featured for the club since the start of last month against Juventus.
In a statement on Thursday, Inter confirmed the 29-year-old had returned to his native Argentina.
It read: "Inter announces that it has defined, by agreement with Southampton, the transfer of Osvaldo to Boca Juniors with the formula of the loan."
Southampton rejected a request by Inter to send the striker back to the Premier League, but they have allowed Osvaldo to make the move to Boca.
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