The Red Devils opted not to renew Pellegrino's contract at the end of the season and he and the club decided to part company with two matches remaining in the first division.
"Gabriel Milito will be Independiente's next coach. He takes charge in the next championship," director Pablo Moyano told local broadcaster TyC Sports.
Independiente, one of Argentina's Big Five clubs, were held 3-3 in a thriller at Gimnasia on Sunday and have no chance of reaching the championship final on May 29.
"It seems logical to me to step aside and, if possible, for the next trainer to take charge next week," Pellegrino told a news conference.
Pellegrino, a former assistant to Rafa Benitez at Liverpool after ending his playing career at Anfield in 2008, joined Independiente from Estudiantes a year ago.
Milito was reserve coach at the Red Devils from 2013-14 and took his first job as head coach at Estudiantes in April 2015, when Pellegrino left for Independiente.
The 35-year-old Milito played for Independiente from 1997 to 2003 before moving to Real Zaragoza after a transfer to Real Madrid fell through over a knee injury.
He was at Barcelona from 2007 to 2011 before playing out his career with a final year back at Independiente. He represented Argentina alongside older brother and former Inter Milan and Racing Club striker Diego Milito.
(Reporting by Rex Gowar; Editing by Tony Jimenez)
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