Samy Thiébault was born May 11, 1978, in Abidjan, Côte d'Ivoire, to a Moroccan mother and a French father; he grew up largely in France and has described his father as "apolitical, therefore right-leaning" against his mother's communist politics. He studied classical music at the Conservatoire de Bordeaux, then earned a master's degree in philosophy with high honors from the Sorbonne in 2001 before turning to jazz full time around age 25. In 2004 he entered the jazz program at the Conservatoire National Supérieur de Musique et de Danse de Paris (CNSM), graduating in 2008.

His discography begins with Blues For Nel (2004), a quintet date credited to the Samy Thiébault Quintet. He was subsequently noticed by saxophonist Lionel Belmondo, who signed him to B-Flat Recordings, the label he and his brother, trumpeter Stéphane Belmondo, had founded; the result was Gaya Scienza (2007), on which Stéphane Belmondo set aside his trumpet to play drums, percussion, and conch shell, an unusual role for him. In 2010 Thiébault founded his own label, Gaya Music Production, releasing Upanishad Expériences as its first project, a suite setting texts by Nietzsche and Baudelaire with narration by actor Jackie Berroyer. Clear Fire (2013) drew wider critical notice, with Le Nouvel Observateur calling his playing "Coltranian in the best sense of the word."

A Feast of Friends (2015), billed to the Samy Thiébault Quartet, reimagined songs by The Doors; Libération wrote that the group "dances somewhere between trance and spiritual communication," and the record carried the quartet on a year-long tour across four continents. Rebirth followed in September 2016, a set of new compositions for quartet that also folded in two arrangements drawn from Maurice Ravel's Ma Mère l'Oye ("Laideronnette, Impératrice des Pagodes," presented twice, as a studio take and an alternate take). The session brought in trumpeter Avishai Cohen as a guest player; Discogs' release-level credit for Cohen carries no guest tag and no track restriction, consistent with the album's own account of the record as "an opportunity to work and record with the great trumpeter." Rebirth was named jazz album of the year by the radio station Fip, and France Inter described Thiébault as one of "the most important, emblematic musicians of his generation."

From 2018 he turned toward a two-part exploration of jazz's Caribbean and Latin roots. Caribbean Stories (2018) was recorded with a Paris-based band including Cuban percussionist Inor Sotolongo, Cuban bassist Felipe Cabrera, and Guadeloupean drummer Arnaud Dolmen. Symphonic Tales (2019) paired his working quartet, tenor plus pianist Adrien Chicot, bassist Sylvain Romano and drummer Philippe Soirat, with the Orchestre Symphonique de Bretagne under conductor Aurélien Azan Zielinsky, adding tablas player Mossin Kawa; the album sets Hindu-inflected themes of self-transcendence inside orchestral jazz arrangements. Awé! (2021) shifted the personnel again, recorded across Miami, Cuba, France, and São Paulo with a mostly American-based band: Cuban drummer Dafnis Prieto, bassist Yunior Terry, electric bassist Jose Armando Gola, pianist Manuel Valera, trumpeter Brian Lynch, and pianist/keyboardist Eric Legnini, plus a small string and woodwind ensemble; it was executive produced in the United States by Brian Bacchus. Thiébault was a finalist for the Académie du Jazz's 2021 Prix Django Reinhardt (French Musician of the Year), an award ultimately won that cycle by Thomas de Pourquery.

He has continued to compose for film and theatre, scoring En Son Absence (2014), Les Autres Soirs (2022), and L'Air de la mer rend libre (2023); the last won the France Musique-Sacem audience award for film music in 2023. He was made a Chevalier of the Order of Arts and Letters in 2024. Since 2013 he has also taught as professor of jazz and saxophone at the Conservatoire de Choisy-le-Roi outside Paris. His most recent album, In Waves (October 2024), is a travel-themed project built around field recordings from Cayenne, Fiji, Laos, Indonesia and the Philippines, recorded mainly at Studios La Buissonne in the south of France with vocalists François Ladrezeau, Cynthia Abraham and Armelle Cippe, and returning drummer Arnaud Dolmen. A further album, The Weather Acoustic, is announced on his own site for a 2026 release.

Thiébault's tenor playing draws direct comparison to John Coltrane in the French press ("Coltranian in the best sense of the word," Le Nouvel Observateur), but his records rarely stay inside a straight post-bop frame for long: across his catalog he has folded in Ravel, Hindu philosophy and Carnatic-adjacent rhythm (tablas), Cuban and Guadeloupean folkloric percussion, a symphony orchestra, and, on his two most recent albums, ocean-themed field recordings and vocal textures. What holds the catalog together is the tenor voice itself and a taste for large-scale conceptual programs, whether a quartet-plus-orchestra suite (Symphonic Tales), a transcontinental personnel roster assembled specifically to match the music's geography (Awé!), or a Doors tribute recast for jazz quartet (A Feast of Friends).