Biggi entered the Universities of Milan and Siena where he studied medieval history and the history of medieval music. At the Schola Cantorum Basiliensis in Basel, Switzerland, he was the first musician to earn the diploma of soloist in medieval lute. In the 1980s, Biggi helped establish two of the most important ensembles devoted to medieval Italian music: Alia Mvsica and Ars Italica. He has also participated in performances with many European ancient music groups: the Ferrara Ensemble of Basel, the ensemble A seis voces based in Paris, the ensemble Micrologus in Assisi, and the Ensemble Hesperion XX of Barcelona. Since 1992, he has directed Basel's ensemble Lucidarium. In both roles of instrumentalist and ensemble director, he has made numerous recordings on the Tactus, Auvidis-Astrée, Polygram, Quadrivium, Digital Empreinte, and Florentia Musicae labels. He has given numerous radio broadcasts and holds seminars and teaches courses in the lute and in the history and interpretation of music of the medieval period.