Enzo, 13, has featured for Madrid's academy teams since 2017.
The teenager confirmed the news in an Instagram post on Saturday, saying "My first contract with the best club in the world. Very happy."
Enzo is a highly rated centre forward who plays for Real Madrid's under-14 side.
He is represented by the agency founded by his father, Group Doze.
Marcelo left Madrid last summer after 15 years at the club, during which he won five Champions Leagues and six LaLiga titles, to join Olympiakos in Greece.
He captained Madrid last season to a Champions League and LaLiga double -- although playing a reduced role on the pitch -- to become the most decorated player in the club's history with a total of 25 trophies won.
Marcelo has had a difficult start to life in Greece, making just two substitute appearances in the Super League so far this season.