Vyacheslav Ganelin, known throughout his career as Slava, was born on December 17, 1944, in Kraskovo just outside Moscow. His family moved to Lithuania in 1948, and he took piano lessons at a Vilnius music school before entering the Vilnius Conservatory, where he studied piano and composition and graduated in 1968. He made his first appearances as a jazz pianist in 1961, during the Khrushchev Thaw, when jazz in the Soviet Union was tolerated in some years and suppressed in others. His earliest commercially issued credits, logged on Discogs, are Lithuanian radio and light-orchestra sessions from 1963 and 1964.

Ganelin built a conventional Soviet composer's career alongside the improvised music. He taught composition at the Vilnius Conservatory, served as music director of the Vilnius Russian Drama Theatre, and wrote for film and stage, including the score to Arunas Zebriunas's 1974 musical Velnio nuotaka (The Devil's Bride), adapted from Kazys Boruta's novel Baltaragis's Mill. The film became one of the defining Lithuanian pictures of the Soviet period and is often described as a Lithuanian answer to Jesus Christ Superstar, though Ganelin himself called the score a "rhythm opera" rather than a rock opera. He also wrote the opera The Red-Haired Liar and the Soldier.

The group that made his name began in 1968, when Ganelin formed a trio with percussionist Vladimir Tarasov and saxophonist Vladimir Rezitsky. Rezitsky left in 1971 and was replaced by Vladimir Chekasin, a reed player from Sverdlovsk, fixing the lineup that ran until 1987 and is known variously as the Ganelin Trio, GTCh, and Ganelin/Chekasin/Tarasov. In 1974 the group became one of the first Soviet jazz ensembles granted salaried residency at the Lithuanian State Philharmonic Society, working under the official designation Contemporary Chamber Music Ensemble. That status carried the right to travel, and the trio played across Eastern and Western Europe as well as Cuba, India, and eventually the United States, an almost unheard-of privilege for Soviet improvisers. They appeared at the Warsaw Jazz Jamboree in 1976 and at the Berlin Jazz Festival in 1980, where a German critic wrote that it was "the most organised and the most professional free jazz" he had heard in years.

The trio's international reputation was built largely by one man outside the USSR. Leo Feigin, a Russian emigre broadcaster in London, founded Leo Records in 1979 and released the trio's Catalogue: Live in East Germany, taped in East Berlin on April 22, 1979, from a tape smuggled out of the Soviet Union. The sleeve carried the line "musicians do not bear any responsibility for publishing these tapes," and Leo Records repeated that disclaimer on subsequent Ganelin releases. Over the following decade Feigin issued the bulk of the trio's catalog in the West, including Ancora da Capo, Con Fuoco, New Wine...., Vide, Baltic Triangle, Con Affetto, and Poco-a-Poco, while Melodiya at home put out Con Anima, Concerto Grosso, Poi Segue..., and Semplice, and the German label Enja issued Non Troppo in 1983. In 1986 the Ganelin Trio became the first Soviet jazz group to tour the United States, seventeen concerts in twenty-one days that opened in New York on a JVC Jazz Festival bill with Lester Bowie's Brass Fantasy and ran through Los Angeles, San Francisco, Chicago, Washington, and Boston. The San Francisco date, June 27, 1986, ended in an unrehearsed set with the Rova Saxophone Quartet, later released as San Francisco Holidays.

Ganelin emigrated to Israel in 1987, which ended the trio. He settled in Jerusalem and became a lecturer at the Jerusalem Academy of Music and Dance, where he has taught jazz solfeggio, composition, music for film and theatre, and individual jazz piano, holding the rank of professor. He assembled a new Israeli trio with bassist Victor Fonarov and drummer Mika Markovitch, documented on Jerusalem February Cantabile (recorded in Jerusalem in February 1989) and Opuses (recorded December 24, 1989). He also recorded solo, on Con Amore and the multitracked On Stage...Backstage, and in duo with the Sephardi and Middle Eastern vocalist Esti Kenan Ofri on On the Edge of a Dream and Birds of Passage.

In 1999 Ganelin founded Ganelin Trio Priority with Lithuanian soprano saxophonist Petras Vysniauskas and German percussionist Klaus Kugel, a group still active decades later and documented on Live in Germany, Live in Lugano, Visions, and Solution. The original trio reunited for a 2001 tour and a set at the Frankfurt Book Fair on October 8, 2002, issued as 15 Year Reunion. Ganelin has kept recording steadily into his eighties, most often with Russian and Lithuanian partners: the trio with saxophonist Alexey Kruglov and drummer Oleg Yudanov (Russian New Music in China, Us, Access Point), a duo with organist Vladimir Homyakov (Neuma), and a Tel Aviv live duo with saxophonist Lenny Sendersky (Hotel Cinema). He directs the international Jazz Globus festival in Jerusalem and continues to write for film and theatre. Ganelin, Chekasin, and Tarasov were awarded the Lithuanian National Prize for culture and arts for 2016, the country's highest artistic honour, presented in 2017.

Ganelin's trio worked as a single composing organism rather than a solo-and-rhythm-section unit, and it used roughly twenty instruments among three players: Ganelin on piano, the Soviet-built basset keyboard, synthesizers, electric guitar, trumpet, and percussion; Chekasin on saxophones, clarinets, basset horn, flutes, and violin; Tarasov on drums, percussion, trumpet, and whistles. Their long pieces were structured suites built out of free improvisation, with folk melody, tango, cabaret, and classical episodes surfacing and dissolving inside them, plus a strong streak of stage theatre carried over from Ganelin's drama-house work. Western critics reaching for comparisons landed on the Art Ensemble of Chicago and Anthony Braxton's compositions, but the trio's discipline was what struck listeners hardest: one writer called it "arguably the world's greatest free jazz ensemble" of the 1970s and 1980s. As a pianist Ganelin is a percussive, motif-driven player who works in cells and repetitions rather than long horizontal lines, and he has never abandoned the composer's habit of shaping an improvisation as a form. His later Israeli and Russian groups apply the same method at smaller scale, adding live electronics and synthesizers to the acoustic piano.