Riccardo Fassi was born in Varese, in Lombardy. He studied music at his hometown's Liceo Musicale before earning a piano diploma at the Conservatorio "L. Perosi" in Campobasso, then went on to study composition and attend jazz seminars. Working out of Rome, he formed his own orchestra, the Tankio Band, in 1983, and it has anchored his career ever since. The ensemble has been voted among Italy's top 10 jazz formations in Musica Jazz magazine's annual critics' referendum in 1991, 1996, 2002, 2003, 2005 and 2007, and Fassi himself was named among the top 10 composer-arrangers of Italian jazz in that magazine's 2007 poll. He has also topped the keyboards category of the JAZZiT Awards on multiple occasions; one contemporaneous biography cites 2012-2014 and his own official website lists 2017-2019, so the exact years are not consistently documented across sources, though the top ranking itself recurs independently in both. As a leader, co-leader and composer he has recorded roughly two dozen albums, seven of them with the Tankio Band, and has performed at major international festivals across Europe, the Americas, Africa and the Middle East. He directed the Jazz Department at the Cherubini Conservatory in Florence from 2004 to 2022, teaching jazz composition and jazz piano.

The Tankio Band's core recorded identity runs through two long-running tribute projects: Plays the Music of Frank Zappa (1995, Splasc(h) Records), followed more than twenty years later by a sequel, Plays Zappa - The Return of the Fat Chicken (2017, Alfa Music, with American vocalist and saxophonist Napoleon Murphy Brock as a guest), and Plays the Music of Eric Dolphy (2005). Its 1989 album Il Principe featured American saxophonist Steve Grossman as guest soloist alongside trombonist Giancarlo Schiaffini, and its 2001 album Serial Killer, a big-band treatment of Ennio Morricone film themes, featured trumpeter Enrico Rava and accordionist Antonello Salis as guests. A 2016 release, Riccardo Fassi Tankio Band Meets Fabio Morgera, was composed, arranged and conducted by trumpeter Fabio Morgera. Across these and the band's other albums (Riccardo Fassi Tankio Band, 1985; Notte, 1991; Seven Pieces for Large Ensemble, 2007) the recurring personnel included trumpeters Claudio Corvini, Aldo Bassi and Giancarlo Ciminelli, trombonists Mario Corvini and Massimo Pirone, guitarist Fabio Zeppetella, bassist Luca Pirozzi and drummer Pietro Iodice, with Gabriele Mirabassi and Flavio Boltro appearing as guests on later and earlier dates respectively.

Fassi's most enduring outside partnership has been with the accordionist and pianist Antonello Salis: the two made the duo album Joining in 1986, a second duo record, Totem - Live at the Vatican Radio, in 1995, and Salis returned repeatedly as a Tankio Band guest (Notte, 1991; the 1995 and 2017 Zappa albums; Serial Killer, 2001). In May 2025, thirty-nine years after their first record together, Parco della Musica Records released Cum Grano Salis, on which Fassi orchestrated Salis's own compositions for a seventeen-piece Tankio Band, including "Random Sequencer," a piano concerto written around him with a solo cadenza. Fassi also led a working piano trio with bassist Gianluca Renzi and drummer Ettore Fioravanti that recorded with the soprano saxophonist Steve Lacy over roughly seven to eight years, released as Dummy (2002, billed "Steve Lacy Meets the Riccardo Fassi Trio"). Trombonist Danilo Terenzi was Fassi's co-leader in the one-off Fassi & Terenzi Quartet, whose sole album, Out of Phase (1988), also featured bassist Massimo Moriconi.

He has also built a body of work in New York: the Riccardo Fassi New York Quintet (2001, YVP Music), recorded at Systems Two in Brooklyn with bassist Dennis Irwin, drummer Adam Nussbaum, vibraphonist Bryan Carrott and baritone saxophonist Gary Smulyan; and the Riccardo Fassi New York Pocket Orchestra's Sitting in a Song (2009, Alice Records), recorded at the same studio with trumpeter Alex Sipiagin, alto saxophonist David Binney, Gary Smulyan again, bassist Essiet Essiet, drummer Antonio Sanchez and trombonist Andy Hunter; Down Beat magazine gave the album four stars. Fassi and Sipiagin later worked together again in Italy, in the electric Riccardo Fassi Analog Trio, alongside bassist Marco Siniscalco and drummer Davide Pettirossi, on Synthi Mental Moog (2019, Jazzit Records). Other credits include L'Amico Immaginario (1998), a duo billing with Gary Smulyan; Solo Trio (2004), co-billed with drummer Leo Cesari and reedman Gabriele Coen; Bemsha (2004, Splasc(h) Records), a quartet with guitarist Luigi Tessarollo, bassist Paolino Dalla Porta and Adam Nussbaum; the solo piano album In the Flow (1993, Amiata Records); and the score to the 2009 film L'amore nascosto, co-written with the conduction pioneer Lawrence "Butch" Morris.

Fassi's writing spans two poles that meet inside the same catalogue: dense, arranged big-band jazz for the Tankio Band, built on tribute programs to Frank Zappa and Eric Dolphy and on his own orchestral commissions, and small-group and duo playing that leans toward free improvisation, heard across his long duo partnership with Antonello Salis and his years recording with Steve Lacy. As a keyboardist he has been described as bringing an unusually creative and coloristic sensibility to the instrument, moving between acoustic piano, Fender Rhodes, synthesizer and, in the Riccardo Fassi Analog Trio, a fully electric analog-keyboard format. His New York-recorded albums, cut with American sidemen including Gary Smulyan, Adam Nussbaum and Alex Sipiagin, sit closer to mainstream contemporary post-bop, while his film scoring work, including a 2009 soundtrack co-written with Butch Morris, connects his big-band arranging to conducted, notated large-ensemble writing.