Born in Berlin to a French mother and an American father, Terrasson's distinctive piano style reflects his old and new influences. In his youth, he spent years studying and listening to recordings by Bud Powell, Bill Evans, and Thelonious Monk. He began playing piano at age five, and his parents were always playing classical music on the stereo. At age 11, he began listening intently to the Billie Holiday and Miles Davis records that belonged to his mother, and at that point, he was hooked on playing jazz piano.

He studied jazz at the Berklee College of Music in Boston with many other new traditionalists as classmates, including people like Danilo Perez. After graduation, he spent a year jamming at clubs in Chicago and New York before hooking up with ensembles led by his mentors, including Arthur Taylor and Betty Carter. At a recording session, Terrasson met Carter. The vocalist told him she needed a pianist to begin a tour the next day, and he accepted, spending nearly a year on the road with her.

Among many other sessions, Terrasson performed on Jimmy Scott's 1996 release, Heaven, for Warner Bros. He also did arranging for that record. Terrasson continues to perform around the world as leader of his own trio, and has made several European and Japanese tours. He's one of the most sought-after sidemen in jazz, constantly in demand for touring jazz bands and recording dates. On his 1996 sophomore effort, Reach, he's ably backed by the same musicians who accompanied him on his debut: bassist Ugonna Okegwo and drummer Leon Parker. Rendezvous followed in 1997, and a year later Terrasson returned with Alive. 1999's What It Is emphasized Terrasson's compositional skills as well as technique. A Paris, an homage to Terrasson's home town, followed two years later. In 2002, Terrasson delivered Smile, a companion piece of sorts to A Paris. He then moved away from ensemble work with his 2007 solo piano album Mirror. In 2010, Terrasson released the lively trio album Push. Terrasson returned in 2012 with the eclectic album Gouache featuring a handful of guest artists including clarinetist Michel Portal, trumpeter Stephane Belmondo, vocalist Cecile McLorin Salvant (winner of the 2010 Thelonious Monk International Jazz Competition), and others.