Honorary Member of UNESCO, the Italo-Latinoamericano Institute, the Real Academia de Bellas Artes (Granada) and Guest Composer of the Brandenburg Academy of Sciences and Humanities (Berlin) amongst memberships of other prestigious international institutions. 

Composer, orchestral director, guitarist, researcher, educator and cultural promoter, Brouwer is one of the most well known musicians of his time. 

Worthy of mention are his directorial roles in the first music department of the Cuban Institute of Arts and Cinematographic Industries (ICAIC) in 1960 and the Musical Theatre of Havana in 1962. He founded and directed the Sound Experimentation Group of ICAIC in 1968. He has been on the jury of many guitar, composition and conducting competitions. He has conducted more than 100 symphony orchestras and chamber groups all over the world. The discography of his music contains more than 600 registered recordings and a catalogue of 300 works that spans nearly all genres and musical forms. 

Brouwer was Principal Director of the Orchestra de Cordoba (Spain) from 1992 to 2001 and Principal Conductor of the National Symphony Orchestra of Cuba from 1981 to 2003. 

He was awarded the "Manuel de Falla" prize in 1998 and Honorary Doctorates from both Havana and Santiago de Chile universities. In its first year of existence in Cuba, Brouwer won the National Music Prize in 1999. In 2003 he was awarded a MIDEM classical music prize in the category of solo/orchestra with his Helsinki Concerto for guitar and orchestra. 

Currently he runs the Leo Brouwer Office in Havana.