Valverde was born in Buenos Aires, Argentina, in 1957, studying there with Manuel Juárez at the National Conservatory. In France, he studied with Dominique Patier (University of Poitiers,1982-1983) and electroacoustic music at the “Groupe de Musique Experimentale de Bourges” (1983-1984).
He attended seminars on musical composition with Helmut Lachenmann. Between 1990 and 1992 he lived in the United States where he continued research on computer-music and composition at the State University of New York at Buffalo as visiting composer.
His music was selected for the “ISCM World Music Days” in Hungary (1986), Germany (1987), Sweden (1994) and Rumania (1999). Awards include the Bourges International Competition 1990 (France), National Foundation of Arts 1988 and National Rostrum of Composers 1984-1985 (Argentina), Forum Jünger Komponisten 1992 (WDR, Germany), among many others.
He has received commissions from and was invited as guest artist at GMEB (France), Hannover School of Music (Germany), Music Academie at Basel (Switzerland), Gaudeamus Foundation (Holland), Logos Foundation (Belgium), McGill and Montreal Universities, Nouvel Ensemble Moderne (Canada), North American New Music Festival (USA), Ensemble 2e2m (France), Ensemble Attacca (Berlin), Leipzig Radio Orchestra, Malmö Symphony Orchestra (Sweden), Danish Chamber Players, Mondrian Ensemble (Switzerland), and Laboratory of Music Research (Buenos Aires). He is co-founder and current co-director of the Centro de Estudios Avanzados en Musica Contemporñea (CEAMC) in Buenos Aires.