Brazil, who was a Forest youth coach, replaces Nick Marshall who was sacked after 16 years of service on Thursday.
Development coach John Pemberton, who only joined Forest in October, was also sacked along with Marshall.
Brazil takes over the running of the academy after guiding the Reds to their second consecutive FA Youth Cup quarter-final.
A club statement from chairman Fawaz Al Hasawi read:
"This season's FA Youth Cup exploits have proved that we have the foundations already in place and we hope that, under Gary's guidance, the first team will soon benefit from that."