Times were hard in Italy after the First World War and in 1927 his father, Enrico, and older brother, Bruno, left for Argentina where they settled initially in Saavedra, a neighbourhood in northern Buenos Aires.
That same year the city of Buenos Aires suffered severe flooding as the River Plate overflowed its banks and the Bragato family lost everything, including José's piano.
In 1930 a colleague of Bruno in the Colón Theatre orchestra, the German cellist and teacher Ernst Peltz, began to give José free lessons on a cello which he provided for him and it was with this instrument that he entered the Manuel de Falla National Conservatory of Music.
Alongside this he was also playing in tango orchestras, including the Orquesta Francini-Pontier formed by the violinist Enrique Mario Francini and the bandoneonist Armando Pontier, and was beginning to compose.
He was a co-founder of the Channel 13 orchestra, together with the Italian musician Lucio Milena, and joined Leo Lipesker and the Primer Cuarteto de Cámara del Tango.
In 1955 Ástor Piazzolla formed his Octeto Buenos Aires and Orquesta de Cuerdas (String Orchestra) and invited José to play the cello as a solo instrument in these Nuevo tango ensembles.
During the period of Argentine military dictatorship from 1976 to 1982, he left Argentina and became principal cellist in the Orquestra Sinfonica de Porto Alegre (OSPA) in Brazil.