United confirmed Rojo’s loan move on their official website on Wednesday evening.
The 29-year-old returns to the club where he started his career in the hunt for game time, having not played for United’s first team since November.
This season he has made nine appearances in all competitions, with three of them in the Premier League.
A statement from United reads: “Manchester United has reached an agreement with Estudiantes for the loan of Marcos Rojo, pending international clearance.
“The 29-year-old defender began his professional career with the Argentinian club in 2008 and he will now finish the 2019/20 season in La Plata, linking up with their head coach Gabriel Milito.
“Rojo joined United from Sporting Clube de Portugal during the summer of 2014 and, since then, he has made 122 appearances for the club, scored two goals and won four trophies.
“In his loan spell at Estudiantes, Marcos will be reunited with a former team-mate of club and country, Juan Sebastian Veron, the former United player who is currently the club’s chairman.
“Everybody wishes our no.16 good luck for the rest of the campaign.”
Estudiantes also announced the return of Rojo on their verified Twitter handle.
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