Gianni Savelli was born in Naples in 1961, the son of a NATO employee, and grew up moving between postings. As a teenager he studied flute, went through rock and jazz-rock, and then switched to saxophone under the influence of John Coltrane. He arrived in Rome around 1980, at about nineteen, joined the Saint Louis Big Band directed by Bruno Biriaco, and by his own account learned the orchestral craft there. Big-band writing became a lasting interest, and it runs through everything he has led since.

For most of the next two decades he worked as one of Rome's busiest session and touring saxophonists. According to his own biography, he toured with Riccardo Cocciante in 1988, with Ornella Vanoni in 1989 and with Luca Barbarossa in 1990, played the Italian dates of Natalie Cole's Unforgettable Tour in 1991 and 2000, and spent 1994 to 1997 on the road with Marina Rei, taking the saxophone solo on her song "Primavera." Discogs corroborates the studio side of that career: credits on Cocciante's Viva! (1988), Marina Rei's self-titled album and the Primavera remixes, Jovanotti's Lorenzo 2002 - Il Quinto Mondo, Renato Zero's Presente (2009) and Antonello Venditti's Tortuga (2015). His biography adds television and festival work for RAI and Fininvest, several Sanremo Festival editions where he shared stages with Ray Charles, Mireille Mathieu and Michael Bublé, and work with Chiara Civello and Sergio Cammariere. Most of the roughly 44 releases under his name on Discogs are pop-oriented sessions and compilations of this kind, which is why he is often described as one of Italy's most eclectic saxophonists; the jazz credits cluster from 2004 onward.

The jazz identity that defines his profile now took shape in 2000, when he formed Media Res, a project meant to gather the different sources behind his playing: rhythms from distant cultures, European harmony and jazz improvisation. The group's first album, catalogued on Discogs as Jazzing Roma (2004, ConcertOne), was followed by Que la fête commence (Alfa Music, 2009), Magellano (Neuklang, 2015) and Alisei (Alfa Music, 2024). Trumpeter Aldo Bassi was on the first three, and the 2015 Magellano lineup added pianist Enrico Zanisi, bassist Luca Pirozzi and drummer Alessandro Marzi. Several pieces on those records won recognition as compositions: his biography lists first prize at the "Scrivere in Jazz" competition in 2010 for "Flying Over the Gocius of Santu Micheli" (the opening track of Magellano), a finalist place at the Artez International Composition Contest in 2011 for "Kirshrot" (on Magellano as "Kirschrot"), and a special mention from the National Academy of Music in Colorado for "Aged Lands." The Que la fête commence closer "Semplice" is dedicated to Yusef Lateef, whom his biography also lists among the international jazz musicians he has worked with.

From 2005 to 2011 he was a member of the Parco della Musica Jazz Orchestra, the resident big band of Rome's Auditorium, under the direction of Maurizio Giammarco. By his own account the orchestra hosted conductors and composers including Bob Brookmeyer, Kenny Wheeler, Maria Schneider, Dave Douglas and Enrico Rava, and made six recordings across some 200 performances. Discogs confirms him in the saxophone section of the orchestra's Jazzitaliano Live 2007 (Casa del Jazz) and on tenor saxophone on "Little Pixie" on Musica Jazz's 2011 To You: Thad Jones compilation, and credits him as composer of "Call" on the orchestra's Open On Sunday (2010). He also plays on the Dino e Franco Piana Jazz Orchestra's Omaggio a Armando Trovajoli (2008), and Discogs lists him among the members of Six Sax, the saxophone ensemble that also includes Javier Girotto and Rosario Giuliani. His biography names Randy Brecker, George Garzone, Bob Mintzer and Jack Walrath among other international jazz collaborators.

Outside the studio, he was musical director of the theatre production Memoriae Temporum (2002) with Paola Gassman and Ugo Pagliai. His own site's biography says that since 2012 he has held the chair in Musical Improvisation Techniques at the L. D'Annunzio Conservatory in Pescara.

Alisei, released in 2024, is the most ambitious Media Res record so far: the quintet of Savelli, trumpeter Fulvio Sigurtà, Zanisi, Pirozzi and Marzi, with a 17-piece jazz orchestra added on two of its six tracks. Jazzfuel, Jazz Views, Jazz Weekly and Bluebird Reviews all covered it; Jazz Weekly heard "Gil Evans-y" orchestral textures next to vintage-sounding hard bop. The piece "Delicati Effendi" is an homage to Bassi, who died in 2020 and had been a principal voice of the group since its start. Savelli and the group presented the album at Rome's Casa del Jazz on December 8, 2024, and announced Frosinone, Rome and Latina dates for February 2025.

Savelli is a tenor player who came to the saxophone through Coltrane and learned ensemble writing in big bands, and the two threads show in his records: small-group playing rooted in hard bop and post-bop, framed by arranged, orchestral writing. Reviewers of Alisei heard vintage-sounding hard bop in the quintet pieces and Gil Evans-like textures in the orchestral pages, and described the album's atmosphere as dark and contemplative. His compositions borrow non-European rhythms, and titles such as "Jali," "Nakuru Lake," "Gujarat," "Sevdah" and "Desejo" reflect the same range. The project also has an environmental streak: Media Res has worked with the World Wildlife Fund on a water-conservation campaign, and Alisei takes its name from the trade winds. Flute and alto flute, his first instrument, appear across the Media Res records alongside tenor and soprano saxophone.