Rojo became the first consolidation of the championship and the Argentine League Cup.
The 30-year-old defender joined the Argentine league champions without the Red Devils announcing the value or duration of the deal.
Rojo spent the second half of last season on loan to Estudiantes and returned to United.
Rojo has only played one match for the club headed by Juan Sebastian Veron, the club that started his career with his shirt from 2009 to 2011.
He played his last match for Manchester United in November 2019
Rojo joined United from Sporting Lisbon in August 2014.
🔴 We’d like to thank Marcos Rojo for his time at United and wish him the best of luck for the future! 🇦🇷#MUFC
— Manchester United (@ManUtd) February 2, 2021
The Argentine won the English League Cup, the Federation Cup, the Community Shield and the European League.
Overall, the 30-year-old left-back played 122 matches and scored two goals.