Jacques-Laurent "Jacky" Terrasson was born on November 27, 1965, in Berlin, the son of an African-American mother from Georgia and a French father, and grew up in Paris, which is why he is described as a French pianist. He began piano lessons at five, studied classical piano at school, and heard jazz through his mother's Miles Davis and Billie Holiday records. In Paris he studied jazz with Jeff Gardner and came to know Francis Paudras, the friend of Bud Powell whose story lies behind the film Round Midnight. As a teenager he was a regular in the city's jazz clubs, and JazzTimes notes that he can be seen in the club audience of Bertrand Tavernier's 1986 film, which starred Dexter Gordon.

Terrasson attended the Berklee College of Music in Boston for two semesters, then worked clubs in Chicago and New York, and settled in New York in 1990. His first recordings included Moon and Sand with the trumpeter Tom Harrell (released in 1991) and sideman dates for Wallace Roney (Seth Air, 1991), Ray Brown (Ray Brown's New Two Bass Hits, 1992), Jesse Davis (As We Speak, 1992) and the drummer Art Taylor (Wailin' at the Vanguard, 1993). In 1993 he won the Thelonious Monk International Jazz Piano Competition. Blue Note's biography says he met Betty Carter at a recording session, was asked to join her for a tour that began the next day, and stayed on the road with her for nearly a year.

A year after the Monk win he signed with Blue Note, where he led a trio with the bassist Ugonna Okegwo and the drummer Leon Parker. The albums Jacky Terrasson (1994) and Reach (1995) were followed by Alive, recorded live on June 14, 1997, at the Iridium Jazz Club in New York and released in May 1998. In between came Rendezvous (released September 23, 1997), a set of standards and pop songs with Cassandra Wilson, and sideman work for Jimmy Scott, on whose Heaven (1996) he also contributed arrangements, and for Dianne Reeves on Quiet After the Storm (1994). What It Is (May 18, 1999) added Michael Brecker and the percussionist Mino Cinélu.

His next two albums made the French half of his background an explicit subject. A Paris... (released February 27, 2000) treated French chanson, among them "Plaisir d'Amour," the theme from Jeux interdits and Jacques Brel's "Ne me quitte pas," as jazz standards, and was recorded in France with mostly French players. Smile (2002) took a similar approach, mixing standards with French songs, and won the best jazz album prize at the 2003 Victoires du Jazz. In between he recorded Kindred (2001) with the vibraphonist Stefon Harris, which was nominated for a Grammy Award for best jazz instrumental album, and in 2003 Blue Note issued Into the Blue, jazz treatments of classical melodies recorded with the flutist Emmanuel Pahud in 2001. Mirror (2007) was an album of solo piano, and Push (Concord Jazz, April 27, 2010) was his first album for that label and included his debut as a vocalist.

In February 2012 he signed with Universal Jazz France and recorded Gouache (2012) with Michel Portal, Stéphane Belmondo, the percussionist Minino Garay and the singer Cécile McLorin Salvant. He moved to Impulse! for Take This (2015), a trio album with guests including the beatboxer Sly Johnson, which was nominated for best jazz album at the Victoires du Jazz, and for Mother (2016), a duo album with Belmondo. In 2019 he returned to Blue Note with 53, a trio album with Ali Jackson, and in December 2021 he performed 53 in an orchestral version with the Orchestre National de Bordeaux at the Opéra de Bordeaux, conducted by Bastien Stil. After moving back to Paris from New York during the pandemic, he started his own label, Earth-Sounds, in 2023; it issued Moving On in 2024, recorded in France and New York with American musicians including Billy Hart and Eric Harland. He has also recorded with Ry Cooder (the Primary Colors soundtrack, Chavez Ravine and My Name Is Buddy) and has worked with Charles Aznavour.

Terrasson's playing is light and quick but carefully controlled, and the writers who have described him compare his speed and control to Bud Powell and his sense of phrasing and breath to Ahmad Jamal, while noting an ear for Ravel, Fauré and Debussy. Blue Note's biography lists Powell, Bill Evans and Thelonious Monk among the pianists he studied closely as a young player. In a JazzTimes interview he said that melody is what holds a piece together, named Keith Jarrett and Wayne Shorter as favorite listening, and called himself a frustrated singer; on stage he often sings or scats along with his own solos. His playing grew leaner over the years, with melodic themes and variations at the center, and his French-song albums, A Paris... and Smile, treat chanson as jazz standards, taking the songs out of their French context and judging them as vehicles for improvisation. In the mid-1990s Blue Note described him as one of the bright young lions of the traditional jazz scene.