"Mauricio Pellegrino is returning home! Welcome Flaco!" said Velez on its official Twitter account on Thursday night, using their former player's nickname.
Pellegrino, 48, began his career as a centre-back with Velez during the Buenos Aires club's golden era in 1990s, winning four Argentine titles and the continental Copa Libertadores.
He ended the decade with a season-long loan to Barcelona, winning La Liga, before joining Rafael Benitez's Valencia where he won two more La Liga crowns and played in two Champions League finals.
He reunited with Benitez at Liverpool for six months in 2005, but was cup-tied for the Reds' epic Champions League victory over AC Milan.