He was born in Bassano del Grappa, Italy, and studied jurisprudence at the University of Padova, but his attention was turned to mineralogy and botany. In 1802 he was appointed professor of botany in the new lyceum of Brescia; but he more especially devoted himself to geological researches in the adjacent districts. The fruits of these labors appeared in different publications, particularly in his Trattato mineralogico e chemico sulle miniere di ferro del dipartimento del Mella (1808) a treatise on the iron mines of Mella. These researches procured him the office of inspector of mines in the recently established kingdom of Italy, and enabled him to extend his investigations over a great part of the country.
In 1811 he produced a valuable essay entitled Memoria mineralogica sulla Voile di Fassa in Tirolo; but his most important work is the Conchiologia fossile subapennina con osservazioni geologiche sugli Apennini, e sul suolo adiacente (2 vols., Milan, 1814), containing accurate details of the structure of the Apennine range, and an account of the fossils of the Italian Tertiary strata compared with existing species. These subjects were further illustrated by his geognostic map, and his Galalogo ragionato di una raccolta di rocce, disposto con ordine geografico, per servire al/a geognosia dell lie/ia (Milan, 1817). His work Dello stato fisico del suolo di Rome (1820), with its accompanying map, is likewise noteworthy. In it he corrected the erroneous views of Scipione Breislak, who conceived that Rome occupies the site of a volcano, to which he ascribed the volcanic materials that cover the seven hills. Brocchi pointed out that these materials were derived either from Mont Albano, an extinct volcano, twelve miles from the city, or from Mont Cimini, still farther to the north.
Several papers by him, on mineralogical subjects, appeared in the Biblioteca Italiana from 1816 to 1823. In the latter year, Brocchi sailed for Egypt, in order to explore the geology of that country and report on its mineral resources. Every facility was granted by Mehemet Ali, who in 1825 appointed him one of a commission to examine the territory of the recently conquered Kingdom of Sennar; but Brocchi, unfortunately for science, fell a victim to the climate, and died at Khartoum.