Estudiantes lost 1-0 at Arsenal under interim coach Martin Zuccarelli and are at the foot of the "Final" championship after three draws from eight matches.
Former Valencia coach Pellegrino is set to sign for the club based in La Plata and be presented to the media next week.
Pellegrino will replace Diego Cagna, who resigned last week.
"Maurico Pellergino will be the first team's new trainer ... The former Velez (Sarsfield) player is coming to the club and his contract with Estudiantes will be until December 2014," the club said on their official website.
Former Estudiantes and Argentina captain Juan Sebastian Veron, now the club's sporting director, was instrumental in the board's choice of the 41-year-old, who was assistant to Rafael Benitez at Liverpool and Inter Milan.
Pellegrino coached Valencia last year but was sacked in December.
As a central defender he spent a decade at Velez, helping them win the South American Copa Libertadores and world club titles in 1994 before moving to Barcelona in 1998, Valencia a year later and Liverpool in 2005.
Estudiantes won their last league title in 2010 and were crowned South American champions for the fourth time the previous year.
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