Picchi was born in Impruneta in the Province of Florence and studied composition under Ignazio Colson.
His first opera, Marco Visconti premiered at the Teatro del Cocomero in Florence in 1838.
Over the course of his career he composed four operas, an oratorio, numerous pieces of sacred music, music for military bands, and two piano fantasias (both published by Ricordi) on themes from Donizetti's La fille du régiment and Pacini's Saffo.
Picchi became the founding editor of the weekly journal Gazzetta musicale di Firenze in 1853, providing critical guidance in its first two years of publication.
The first had essays on music theory and criticism, while the second focused on reviews of noteworthy performances in Italy and the rest of Europe as well as literary and biographical articles.