He studied double bass with Fernando Grillo and composition with Fausto Razzi and Salvatore Sciarrino. From an early age he was interested in the double bass as a solo instrument and in promoting new trends in contemporary European and American music. In 1983 he founded the Rassegna di Nuova Musica  in Macerata. He has been described as "a tremendous bassist, a fearless improviser, and a gifted composer".
The many composers who have written for him include Brian Ferneyhough, Salvatore Sciarrino, Sylvano Bussotti, Iannis Xenakis, Fernando Mencherini, Gérard Grisey, Giacinto Scelsi, Julio Estrada. He worked for a long period with Luigi Nono.
He worked closely with the musician Terry Riley, as well as with choreographers and dancers such as Virgilio Sieni, Patricia Kuypers, Hervé Diasnas, the poets Edoardo Sanguineti and Gian Ruggero Manzoni, the philosopher Giorgio Agamben, the artist Gianni Dessì and the director and playwright Rodrigo Garcia. He played regularly with Rohan de Saram and Markus Stockhausen.
From the 1990s he taught master classes and seminars at the Shepherd School of Music at Rice University, University of California Berkeley, Stanford University, Oberlin Conservatory, Musikhochschule Stuttgart, Conservatoire de Paris, Milan Conservatory, etc. In 1996 he taught double bass at Darmstadt Ferienkurse.
- 1997 - Lazy Afternoon among the Crocodiles - Terry Riley & Stefano Scodanibbio (Pierrot Lunaire)
- 1998 - Voyage That Never Ends (New Albion)
- 1998 - One says Mexico
- 1999 - Postkarten - Stefano Scodanibbio & Edoardo Sanguineti
- 2000 - Geografia amorosa
- 2001 - Six Duos (New Albion)
- 2001 - Visas per Vittorio Reta
- 2004 - My new address (Stradivarius)
- 2005 - Diamond Fiddle Language - Terry Riley & Stefano Scodanibbio (Magonza/Wergo)
- 2006 - Visas per Vittorio Reta - (Le Lettere, Florence)
- 2010 - On Debussy's Piano And... - Thollem/Scodanibbio (die Schachtel)
- 2010 - Oltracuidansa (Mode Records, New York)
- 2013 - Reinventions - Quartetto Prometeo (ECM records)
- Johan Lohse, Double Bass Guide
- Sequenza 21, 13 January 2012
- The Strad
- Scodanibbio in Discogs
- The Wire, 12/01/2012