Vinicus, who turns 18 on Friday (AEST), initially signed for Los Blancos last May in a £40.5m transfer from Flamengo.
Brazilian law prohibited him from leaving prior to his 18th birthday, and he will now join Julen Lopetegui's men for pre-season next week.
Posting on Instagram, Vinicius wrote: ''On Friday I go to Madrid and I am a little nervous and anxious for this new stage of my life.
''A new challenge that I am going through, being so young, that God can bless me and also my family, that my friends can help me more. This is my biggest dream."
Vinicius managed four goals and three assists in 11 Serie A starts last season, and moves to the Spanish capital with much fanfare as Madrid begin the post-Cristiano Ronaldo era after the Portugal star's move to Juventus.