Raddi was apprenticed to a druggist, but obtained employment in the Museum of Natural History of Florence. Ferdinand III, Grand Duke of Tuscany, afterward became his protector, and in 1817 sent him to Brazil to study the cryptogams of the country. Raddi explored the basins of Orinoco and Amazon Rivers, and formed a collection of plants and animals.
In 1828 he was appointed a member of the commission that was charged with studying the Egyptian hieroglyphs under the direction of Champollion, but he was taken sick and died in Rhodes on his return to Florence.
His works include Crittogame Brasiliane (2 vols., Florence, 1822) and Plantarum Brasiliensium nova genera et species novae vel minus cognitae in which he described 156 new species of ferns, etc. (1825).