Bavouzet was born in Lannion, France, in 1962. He studied music at the Paris Conservatory with Pierre Sancan. In 1986, Bavouzet won the Beethoven International Competition in Cologne. Three years later he was given the Steven de Groote Memorial Award for best chamber music performance at the Van Cliburn Competition. While Bavouzet enjoyed reasonable success in the wake of these triumphs, including his appearance on a 1993 Accord release of works by Stockhausen, his breakthrough came in 1995 when he debuted with the Orchestre de Paris at the invitation of Georg Solti. In a 1998 concert with the Orchestre de Paris, Bavouzet collaborated with Pierre Boulez, a conductor with whom he would make many subsequent appearances, both in France and abroad. Bavouzet has concertized throughout Europe, the U.K., U.S., and Asia, and has appeared with many leading conductors, including Gergiev, Ashkenazy, Boulez, and Gianandrea Noseda. Bavouzet distinguished himself further when in 2009 he played the challenging five Prokofiev concertos over two concerts with the Warsaw Philharmonic Orchestra and conductor Antoni Wit. Also in 2009, Bavouzet premiered a work dedicated to him, the Bruno Mantovani piano concerto, The Book of Jeb, at the Piano aux Jacobins International Festival in Toulouse. Bavouzet's repertory extends to individual works by Liszt, Tchaikovsky, and Pierné. Bavouzet's career has continued on the ascent, not least because of his considerable activity in the recording studio. He recorded the complete piano works of Ravel to acclaim for MDG in 2003. For his initial project with Chandos, he issued the complete piano works of Debussy in 2006, with critics broadly approving each release. In 2008, he began recording the complete piano sonatas by Beethoven, the first of which was released in 2012. In 2010, he launched a cycle of the complete Haydn sonatas, with Vol. 8 being released in 2019. Alongside the Haydn cycle, Bavouzet began a survey of Mozart concertos in 2016, issuing Vol. 4 in 2019.
Bavouzet has won awards from Grammophon and BBC Music magazines, as well as the Diapason d'Or and the Choc de l’année.