Glauco Venier was born on 8 September 1962 in Sedegliano, in the province of Udine, in Friuli. He graduated in organ from the Conservatorio Jacopo Tomadini in Udine in 1985, then turned to jazz, studying privately with the pianist Franco D'Andrea and later winning a scholarship to Berklee College of Music in Boston, where Italian Wikipedia has him working with the pianist Ray Santisi. He was a finalist at the Thelonious Monk Competition in Washington in 1989, according to ECM's biography, and has led his own bands since 1990. He teaches jazz at the Udine conservatory.

His first record, Finlandia (Sentemo, 1991), is a set of his own pieces with the flutist Massimo De Mattia. In the mid-1990s he was in a piano trio with bassist Salvatore Maiore and drummer Roberto Dani, which recorded L'Insiùm (Nota, 1996) at Hendrix Studios in Koper, a program of Friulian material with texts by Pier Paolo Pasolini and Amedeo Giacomini in the booklet. That trio grew into larger forms: Seasons (Nota, 1999) adds the Diapason Chamber Orchestra for four movements, one per season, and Gorizia (Artesuono, 2000) brings in a string quartet, the soprano saxophonist Klaus Gesing and the trumpeter and flugelhorn player Kenny Wheeler, who also wrote its liner notes. In the same years he was the pianist on records by other Friulian and Italian bandleaders: Massimo De Mattia's Poésie Pour Pasolini (1993) and The Silent Drama (1995) with bassist Giovanni Maier, Enzo Pietropaoli's Stolen Songs (1998) with guitarist Battista Lena and singer Maria Pia De Vito, Roberto Dani's Images (1999), and the U.T. Gandhi Ensemble's Cjale Ce Sere (Nota, 1998), a Friulian big-group record on which Enrico Rava plays trumpet alongside Giorgio Pacorig, Bruno Romani and Daniele D'Agaro. Rava also wrote the liner notes for Mufloni (Splasc(h), 2000), the quintet album Venier made with trumpeter David Boato, saxophonist Marcello Allulli, Maiore and Dani.

In 2001 he recorded Ides Of March (Artesuono) as a duo with the alto saxophonist Lee Konitz, sixteen tracks that run from "Bird Live," "Solar" and "Cherokee" through improvisations to a suite of four elements. The same period brought the group that made his international name. Singer Norma Winstone sang on Dani's Images (recorded October 1998), and with Gesing she and Venier recorded Chamber Music (EmArcy, 2003) at Artesuono in Cavalicco in June 2002. The Norma Winstone Trio then moved to ECM, where Manfred Eicher produced Distances (2008, recorded April 2007 at Artesuono in Udine), Stories Yet To Tell (2010) and Dance Without Answer (2014, recorded in Lugano). Distances was nominated for the Grammy for Best Jazz Vocal Album at the 51st Grammy Awards in 2009; Cassandra Wilson won. Venier also plays on Winstone's ECM film-song album Descansado (2018), with Gesing, the cellist Mario Brunello and the percussionist Helge Norbakken.

His own projects in these years lean on repertoire and on place. Serenade (Artesuono, 2002) arranges the Friulian composer Arturo Zardini for the Coro del Friuli Venezia Giulia. Intermezzo (Artesuono, 2007) is a piano trio with the Russian bassist Yuri Goloubev and the drummer Asaf Sirkis, who also plays four tracks of the Goloubev duo record Hommage À Duke (Caligola, 2007), eleven pieces by Duke Ellington. Glauco Venier Suona Frank Zappa (Music Center, 2008) is a ten-piece band playing twelve compositions by Frank Zappa, recorded at Artesuono in July 2005. Waits (Artesuono, 2013) is a quartet album listed on Discogs under the Glauco Venier 4tet with trumpeter Flavio Davanzo, drummer Luca Colussi and bassist Alessandro Turchet, and Dodici Musiche Per Dodici Quadri (Artesuono, 2013) is a solo piano record made in the church of San Martino in Artegna.

The larger-scale writing continues in Symphonika (Artesuono, 2014), Friulian folk themes composed by Venier and orchestrated by the guitarist Michele Corcella for the Mittelfest Big Band and the F.V.G. Mitteleuropa Orchestra under Walter Themel, with Winstone, the tenor saxophonist Matthias Nadolny and the trumpeter Uli Beckerhoff as soloists. The big band's brass and reed sections include Achille Succi, Filippo Vignato and Turchet. His own site's biography mentions a related work, Antiche Danze, made with the WDR orchestras in Cologne. With Corcella he then reworked the dance book of the Renaissance composer Giorgio Mainerio for the L'Insiùm ensemble on Mainerio! (Artesuono, 2017), with Winstone as special guest on four tracks and Federico Pierantoni on trombone and euphonium.

Miniatures (ECM, 2016) is his solo record for ECM: fifteen pieces for piano and struck metals, recorded in December 2013 at the Auditorio Stelio Molo RSI in Lugano and produced by Eicher. Venier plays the piano together with gongs, bells and sound sculptures made by the artists Harry Bertoja and Giorgio Celiberti, and the program mixes his own music with pieces inspired by Komitas, Gurdjieff and Dufay. Discogs files it under Classical and Contemporary, and it sits at the chamber end of his catalogue.

Recent years have brought a pair of projects with a more song-like ear. Dialogo Espressivo (Parco della Musica Records, 2021) is a duo of eleven originals with the trumpeter Giovanni Falzone, whose tracks include tributes to Kenny Wheeler and Tomasz Stanko. Suite Per Pier Paolo (Artesuono, 2022), recorded on 20 and 21 December 2021, sets Pasolini's Friulian world for piano, the guitarist Francesco Diodati, the saxophonist Marcello Allulli and the singer Alba Nacinovich. Diodati and Allulli were already his colleagues on Allulli's Hermanos (2012) and MAT (2014). He also produced pianist Emanuele Filippi's Musica Fragile (Artesuono, 2020) and, in 2000, the trio album Colussi Franceschini Chiarion.

Italian Wikipedia's biography lists further collaborations, among them the bassist Marc Johnson, the trumpeter Paolo Fresu and the saxophonist Stefano Di Battista; these appear as stage credits and are not itemized on records. His own site lists concerts at the Musikverein in Vienna, the Barbican in London, the Olympia in Paris and La Fenice in Venice, and broadcasts for RAI, the BBC and Austrian radio.

Venier writes as a pianist-composer more than as a bebop soloist. The Winstone trio repertoire is a mix of his own settings, film songs and Friulian folk melodies, in a chamber texture where the piano, soprano saxophone or bass clarinet and voice share the lead; ECM's biography describes him as a pianist, composer and arranger who adapts materials from Friulian sources. Friuli is the recurring subject: Pasolini's poetry on L'Insiùm and Suite Per Pier Paolo, Zardini's songs on Serenade, folk themes on Symphonika, and Mainerio's 16th-century dances on Mainerio!.

The jazz references run through the tribute and standards records. He has recorded the music of Duke Ellington, Frank Zappa and, with Gesing, standards on Play Songs, and he has made duo and guest sessions with the elder jazz figures Lee Konitz and Kenny Wheeler. Classical training shows in the organ diploma, the Bach transcriptions of Play Bach with Gesing, and the orchestral scores, and at the far edge of his catalogue Miniatures leaves a jazz rhythm section behind entirely. Most of his records are tagged Jazz on Discogs, and the ECM trio, the Konitz and Wheeler sessions and his teaching post in jazz keep him in that world.