He was born in Florence and studied with Giorgio Santi (1746–1822) and Adolfo Targioni Tozzetti (1823–1902). In 1798 he published Flora Pisana (flora of Pisa); in 1801 the first edition of Trattato degli alberi della Toscana (treatise on the trees of Tuscany); in 1808 Botanicon Etruscum (botany of Etruria); and in 1818 Flora Italiana (flora of Italy). He taught physics and botany at the University of Pisa and directed the botanical garden there from 1814. In 1816, he was elected a member of the Royal Swedish Academy of Sciences.
His son was the geologist and ornithologist Paolo Savi (1798–1871).