Brouwer was born in Havana and went to the United States to study music at the Juilliard School where he was taught composition by Stefan Wolpe. He was influenced by modernist composers such as Luigi Nono and Iannis Xenakis and used indeterminacy in works such as Sonograma I. Later works have tended to be more minimal.
Brouwer has held a number of official posts in Cuba, including directorship of the Cinema Institute of Cuba's music department. Among his works are a number of works for solo guitar, a number of guitar concertos and over forty film scores.