Rojo, 30, spent the second half of last season on loan with his first club Estudiantes.
But he has now made a permanent switch to Buenos Aires-based Boca who are reigning Argentine champions.
United signed Rojo from Sporting Lisbon in 2014. He went on to make 122 appearances and scored twice.
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United said: “We’d like to thank Marcos Rojo for his time at United and wish him the best of luck for the future.”
Rojo will link up with former United star Carlos Tevez at La Bombonera who is a legend at his hometown side.
Earlier this week reports suggested United were set to terminate Rojo’s contract.
The Argentina international signed his latest £80,000-a-week deal in March 2018 but started only five Premier
League games since and was not fancied by boss Ole Gunnar Solskjær