Francesco Ponticelli was born in Arezzo, Tuscany, in 1983. He started on guitar at six, picked up electric bass around 1999 to play in a local blues band, and switched to double bass in the early 2000s. He trained at Siena Jazz, where his teachers included Paolino Dalla Porta, Franco Fabbrini, Furio Di Castri and Piero Leveratto, and he began working around Tuscany with Stefano "Cocco" Cantini, Mirko Guerrini and Nico Gori while still a teenager.

In 2005, Enrico Rava recruited him to found a new touring band, billed as Enrico Rava New Generation. The group's live album, released as Jazzitaliano Live 2006 on Casa del Jazz, was distributed through the newspaper chain behind la Repubblica and L'Espresso and reportedly sold around 40,000 copies, an unusual number for an Italian jazz record. The following summer, 2006, Ponticelli was artist in residence at Umbria Jazz with the Giovanni Guidi Trio, recording Tomorrow Never Knows for the Japanese label Venus Records; a second Guidi date, Indian Summer (C.A.M. Jazz, 2007), followed with drummer João Lobo and saxophonist Dan Kinzelman. In 2007 he also joined Gianluca Petrella's Cosmic Band, recording the two-volume live set Coming Tomorrow (Spacebone Records, 2009 and 2012) alongside Guidi on piano.

That same 2009 also produced one of the most-documented sideman credits of his early career: double bass on tracks 7 to 11 of Yakir Arbib's debut album Yakir Portrait (Philology), paired with drummer Roberto Giaquinto as one of three rotating Italian rhythm sections on the record, alongside Enzo Pietropaoli and Marcello Di Leonardo (tracks 3-6) and Massimo Manzi and Massimo Moriconi (tracks 1-2). The Fabrizio Sferra Trio's Rooms (EmArcy/Universal, 2009), again with Guidi on piano, dates from the same busy year.

Ponticelli made his own leader debut in 2014 with Ellipses (Tǔk Music), a sextet record with Kinzelman, guitarist Francesco Diodati, trumpeter Mirco Rubegni and vocalist/violinist Luisiana Lorusso, produced by Paolo Fresu, whose label has carried nearly all of his subsequent leader work. By this point he had also founded Il Cicaleto Recording Studio in Arezzo, which he still directs as an engineer and producer for other Tuscan and Tǔk-affiliated artists. Kon-Tiki (2017), a tighter quartet date with pianist Enrico Zanisi, Kinzelman and drummer Enrico Morello, was executive produced by Fresu and is generally considered his strongest leader statement to date.

2021 was his busiest year on record: Heroes Expanded, a David Bowie tribute billed jointly to Fresu, vocalist Petra Magoni, Petrella, Diodati, Ponticelli and drummer Christian Meyer; and Xenya, a five-way collective co-led with Giaquinto, trumpeter Cosimo Boni, saxophonist Daniele Germani and pianist Alessandro Lanzoni, recorded and engineered by Ponticelli himself at Il Cicaleto. The Giaquinto partnership also reached the stage directly: on July 29, 2019, Arbib, Giaquinto and Ponticelli played a trio date at the Maschio Angioino in Naples as part of the Summer Live Tones festival. In 2023 he released Megapascal (Tǔk Music), his first work to combine voice, words and music, built around vocalist Samuele Cyma, harpist Stefania Scapin, drummer Giovanni Iacovella and a string quartet, and mastered at Sundlaugin Studios in Iceland (the studio built by Sigur Rós). In 2024 he joined Rava's new quintet, the Fearless Five, alongside trombonist Matteo Paggi, Diodati and drummer Evita Polidoro, recording at Rome's Casa del Jazz for Parco della Musica Records; the resulting album and the band itself were both voted best of the year in the 2024 Top Jazz critics' poll run by Musica Jazz.

Ponticelli works comfortably on both sides of a divide that runs through Italian jazz: he is a first-call acoustic bassist for mainstream post-bop leaders like Enrico Rava and Giovanni Guidi, and at the same time a fixture of the more exploratory, electronics-friendly Tuscan scene built around AUAND Records and Tǔk Music, where he plays electric bass, samples and effects alongside his double bass. His own leader records track that same range, from the horn-and-guitar sextet writing of Ellipses to the harp-and-string-quartet chamber-pop of Megapascal, which the label has called some of the most interesting and innovative composing in Italian jazz. Running his own studio, Il Cicaleto, since the mid-2010s has also made him a working producer and mixing engineer for other artists on the same scene, a second career that runs parallel to his playing.