Simone Graziano was born and raised in Florence. He graduated with top marks in classical piano from the Conservatorio "Luigi Cherubini" in Florence under Maestro Stefano Fiuzzi, and studied jazz composition and arrangement at Berklee College of Music in Boston. He has worked or studied with American pianists John Taylor, Kenny Wheeler, Mulgrew Miller and Aaron Goldberg, and with Italian pianists Riccardo Fassi, Enrico Pieranunzi, Stefano Bollani and Franco D'Andrea; these are named in his own biography as teachers or mentors, without an independently verified Discogs recording credit tying him to any of the four. He has taught piano and ensemble at the Siena Jazz Foundation since 2011 and has been a jazz piano professor at Siena Jazz University since 2014.

He made his recorded debut as a leader with Lightwalls (Dodicilune, 2010), a trio session with bassist Ares Tavolazzi and drummer Stefano Tamborrino. He then built his main working group, the quintet Frontal, with American alto saxophonist David Binney and tenor saxophonist Chris Speed (later replaced by Dan Kinzelman), bassist Gabriele Evangelista and Tamborrino on drums, recording three albums for the Italian label AUAND: Frontal (2013), Trentacinque (2015) and Sexuality (2019, by which point Kinzelman had taken over the tenor chair and guitarist Reinier Baas had joined). Musica Jazz magazine's Top Jazz critics' poll named Graziano a top new talent in both 2013 and 2014, and voted Frontal among Italy's ten best working jazz groups in the same period. Between the first two Frontal albums he also recorded a second trio record, Snailspace (AUAND, 2017), with bassist Francesco Ponticelli and drummer Tommy Crane.

Alongside his own leader catalog, Graziano has recorded steadily as a sideman. He plays piano in the Francesco Cusa Trio on drummer Francesco Cusa's From Sun Ra To Donald Trump (2017, Clean Feed), alongside Evangelista and saxophonist Carlo Atti, and plays electric piano and synthesizer in saxophonist Beppe Scardino's ten-piece ensemble on BS10 Live in Pisa (2018, AUAND). In 2020 he was one of the credited musicians, alongside guitarist Cristiano Arcelli, bassist Francesco Ponticelli and Quartetto Mirus, on vocalist Cristina Zavalloni's For The Living (Encore Classical Music & Jazz), a collaborative session built with Norwegian producer Jan Bang and guitarist Eivind Aarset. In 2016 he also arranged for the sextet Purple Whales on Hendrix, a various-artists tribute compilation released by Casa Del Jazz and L'Espresso under the "Giovani Leoni" series banner.

Embracing the Future (AUAND, 2021), his seventh album as a leader, is his first for solo piano. He recorded it himself at home on a Yamaha C3, with two omnidirectional microphones placed inside the instrument, close enough to the hammers to capture the piano's own mechanical noise along with the notes. He remains active as both a leader and a sideman, with a new project, EMEM, released on AUAND in 2026.

Graziano's own catalog sits mainly in a contemporary, composition-driven strain of post-bop: Discogs tags his leader albums "Contemporary Jazz," with Frontal's two earliest records additionally carrying "Free Jazz" and "Free Improvisation" style tags, a mark of the American alto and tenor saxophonists (David Binney, Chris Speed, later Dan Kinzelman) he built the group around. Sexuality and Snailspace lean further toward electric textures, with Graziano doubling on Fender Rhodes, synthesizer and electronics alongside acoustic piano. Embracing the Future, his 2021 solo record, is a clear departure from the quintet format: a set of original pieces for prepared and close-miked solo piano, foregrounding the instrument's own mechanical sound rather than a band arrangement.

His side work shows a second, more overtly free-leaning strand, through Francesco Cusa's and Beppe Scardino's AUAND and Clean Feed circles, both artists whose own catalogs sit further toward free jazz and free improvisation than Graziano's own leader records. As an educator, he has held a jazz piano teaching post at Siena Jazz University since 2014, after piano and ensemble teaching at the Siena Jazz Foundation from 2011.