Massimo Moriconi was born May 20, 1955, in Rome. He began playing bass at thirteen and went on to study classical double bass at the "Licinio Refice" Conservatory in Frosinone. By the late 1960s he was already working as a sideman on Rome's jazz circuit, backing early figures in Italian jazz including Marcello Rosa, Armando Trovajoli, Nicola Arigliano, Lelio Luttazzi, and pianist Romano Mussolini (son of the Fascist dictator and himself a working jazz musician); a 1982 trio session billed to "Trio Romano Mussolini, Massimo Moriconi, Pici Mazzei Plus Eddy Palermo, Wilfred Copello" documents that circle on record.

His first outing as a leader, Bass in the Sky (Lupus, recorded November 1981 at Titania Studios, released 1982), paired him with pianist Enrico Pieranunzi, drummer Bruno Biriaco, and trombonist Birch Johnson, with liner notes contributed by bassist Giovanni Tommaso. Around the same period he entered Chet Baker's working circle in Italy: Discogs credits him as the bassist, alongside pianist Michel Graillier, on Live From the Moonlight, a trio session recorded in 1988, the year of Baker's death, and issued on the Italian label Philology. He turns up on further Baker-related archival releases as well, including the compilation In Italy and the reissued Live in Stockholm 1983 (credited to the Chet Baker-Hank Jones Quartet).

Moriconi's longest-running musical relationship was with pianist Renato Sellani (1926-2014). Their duo album Doppio Passo (Carosello, 1988) opened a partnership that continued for more than two decades, through the Renato Sellani Trio's prolific run of Philology releases in the 2000s: I Wish I Knew and Standards (both 2005, with drummer Massimo Manzi and, on the former, tenor saxophonist Gianni Basso), Blues For Chet (2007), and Gershwin! (2007, adding trumpeter Enrico Rava and vocalist Tiziana Ghiglioni), among many more tribute and songbook dates for Italian composers. Producer Paolo Piangiarelli's Philology also paired Moriconi and Manzi with a run of visiting American names during the same years: Phil Woods, on the Phil Woods Trio's Just Friends (recorded 1994, released 1997, with Sellani on piano), and both Woods and Lee Konitz together on the Phil Woods-Lee Konitz Quintet's Play Woods and Play Konitz (both 2004, recorded live at the Umbria Jazz Festival). He also recorded live with alto saxophonist Massimo Urbani's quartet on September 26, 1983, at Teatro Rossini in Civitanova Marche, a date issued in 2000 as Max Leaps In, and appears on Franco D'Andrea's Round Riff & More 2 (2003), a two-bass session alongside Ares Tavolazzi.

His most ambitious leader date, D'Improvviso (MBO, 2001), gathered Phil Woods, saxophonist Eric Marienthal, flugelhornist Franco Ambrosetti, pianist Danilo Rea, Sellani, and vocalists Mina and Fabio Concato; Moriconi is credited on double bass, electric bass, and mandobass, plus piano on some tracks, and as a co-writer of several pieces. In 2019 he formed a trio with Rea and drummer Alfredo Golino for Tre Per Una, a set of Mina-songbook arrangements released on PDU/Warner Music Italy, Mina's own label, and recorded a duo album, Doppio Vita, with singer Emilia Zamuner the same year. Alongside his jazz work, Moriconi built a long parallel career as one of Italian pop's most in-demand session bassists, playing on Mina's studio recordings for decades (his own biography dates the relationship to 1983, though the earliest credit independently confirmed here via Discogs is 1996) and working with singer-songwriter Fabio Concato since 1993, plus sessions for Fabrizio De André and others.

In 2009 he was one of three rotating Italian rhythm sections on pianist Yakir Arbib's debut leader album, Yakir Portrait (Philology), playing double bass with drummer Massimo Manzi on the record's first two tracks, while its remaining nine tracks split between two further bass/drum pairings.

Moriconi's reputation rests less on a leader discography than on being one of the most trusted rhythm-section anchors in Italian jazz: Paolo Piangiarelli's Philology label paired him and drummer Massimo Manzi with a run of visiting American names through the 1990s and 2000s specifically because the two could hold a mainstream, standards-based pulse behind very different frontline styles, from Phil Woods's hard-driving bebop alto to Lee Konitz's oblique, cool-toned lines to Chet Baker's spare balladry. That same reliability made him a natural crossover choice for Italian pop sessions; he has anchored Mina's studio dates for decades and become a first-call bassist for singer-songwriters, and press biographies (including his own Spotify artist bio) credit him with film-scoring session work for composers Ennio Morricone and Nicola Piovani, though specific film titles were not independently confirmed here. In 1995 Guitar Club magazine's national readers' referendum named him Italy's best double bassist and best studio session bassist, and in 1996 Chitarre magazine's readers voted him the country's best jazz-fusion bassist.