Marco Gallesi was born in Turin in 1954. He began classical music studies as a child, and in the early 1970s he turned toward jazz and rock on electric bass. He was one of the six musicians who founded Arti & Mestieri (also written Arti e Mestieri) in Turin in 1974, alongside drummer Furio Chirico, guitarist Gigi Venegoni, violinist Giovanni Vigliar, saxophonist Arturo Vitale and keyboardist Beppe Crovella. The band made its debut at the Re Nudo festival at Parco Lambro in Milan that year and recorded its first album, Tilt, for Cramps Records, followed by Giro di valzer per domani (1975), the record on which the group leaned hardest into jazz-rock. Gallesi plays bass on both.

After that second album he and Venegoni left the band, though Gallesi still appears on the third, Quinto Stato (1979), credited on bass and as composer of one piece. It was the recording debut of the young Turin trumpeter Flavio Boltro. In Turin in 1975 Gallesi had formed Esagono with keyboardist and cellist Marco Cimino, a former member of Errata Corrige, and drummer Giorgio Diaferia, who came from Combo Jazz, a band aiming for the electric jazz of Joe Zawinul and Wayne Shorter. Its only album of the decade, Vicolo (Mu, UM 101), is an instrumental jazz-rock record cut at Venegoni's Studio G.V. in Turin, with Claudio Montafia on guitar and flute, Aldo Rindone on electric piano and Minimoog, and Vitale, Vigliar and Venegoni sitting in as guests from Gallesi's old band. He is credited on bass, fretless on at least two tracks, and co-wrote two pieces: the title track with Montafia and "Araba fenice" with Cimino. Italian Wikipedia describes the album as recalling Weather Report and the Italian group Perigeo, and says the band moved toward a more openly jazz sound in the early 1980s, taking in Boltro on trumpet, Claudio Bonadè on saxophone, Enrico Cresci on guitar and Massimo Artiglia on piano, before it dissolved.

In the early 1980s Gallesi performed in Italy with the Brazilian percussionist Dom Um Romão, who had played in Weather Report, during Romão's stay in the country. From 1992 to 1996 he worked mainly as an arranger and producer looking for new talent, and in 1997 he produced, arranged and played bass and guitar on the pop-rock album La mia vita non è qui by the singer-songwriter Cristiano Parato.

In 1998 he rejoined the reunited Arti & Mestieri. The reunion lineup recorded Murales (Electromantic Music, 2001), on which Gallesi wrote two pieces, along with the archival collection Articollezione (2001) and the double live album Live / 1974-2000 (2003). He also played bass on Chirico's own Furiosamente (2001). He left the band in the early 2000s and was replaced on bass by Roberto Cassetta.

His solo album Riff (Electromantic Music, ART 9013) is built around his electric bass and includes pieces titled "Giants Step," "Little Wing" and "Besame Mucho," plus one called "Quarto di luna." Esagono came back as well. Vicolo was reissued on CD by Electromantic Music, and 2 (2007) paired two new studio tracks with a live set recorded on February 25, 1977. Apocalypso (2008) brought Gallesi, Cimino and Diaferia together with soprano saxophonist and clarinetist Diego Mascherpa and violinist Lautaro Acosta. Gallesi plays bass on nearly all of it, wrote four pieces and doubles on acoustic guitar on the closing track, and the album includes a version of Ennio Morricone's "Metti una sera a cena." The band toured internationally, with concerts in Tokyo in 2010, and Solid Records reissued Apocalypso in Japan on January 26, 2022. Esagono's later albums Wine Notes and Dylanology feature other bassists.

Gallesi is also a novelist. SBC edizioni of Ravenna published his noir Quarto di luna in 2008 and Come doveva andare secondo Roar in 2009.

Gallesi is an electric and fretless bassist whose work sits where Italian progressive rock meets jazz-rock and fusion. Arti & Mestieri is usually filed with Italian progressive rock, and Discogs tags Tilt as prog rock and the later albums as both jazz-rock and prog, so the jazz side of his career is a fusion story rather than a mainstream one. It is clearest in Esagono, whose first album is tagged jazz-rock on Discogs, whose 2008 comeback is tagged fusion and jazz-rock, and whose stated models were Zawinul, Shorter and Weather Report. He also writes: he has composer credits on records by both bands, and Riff shows him taking on rock, jazz and Latin repertoire alongside his own music.