In a review for AllMusic, Thom Jurek wrote that the album "is not for the Jarrett beginner, but for seasoned fans of his many solo recordings, that are, after all, responsible for a sizeable portion of his legendary reputation.

"[4] The Guardian's John Fordham noted that "everything from the softest improvised ballads to the most exuberantly hard-stomping blues draw grateful accolades – the sound of an audience's thanks for a one-off music that belonged only to their presence with Jarrett, in that space, on that unique evening.

"[6] Mike Jurkovic, writing for All About Jazz, called the album "a remarkable listen," and stated: "Bordeaux Concert feels like it has always been there.

"[3] In an article for The Daily Telegraph, Ivan Hewett remarked: "If this album turns out to be Jarrett's farewell, it will be a more than worthy one.

"[8] Associated Press writer Steven Wine praised the album's "astounding mix of intensity, introspection and invention," and commented: "Structure and pacing are a marvel as Jarrett's on-the-spot composition swings between gorgeous lyricism and dissonant, distressed chromatic explorations that abandon tempo... One yearning melody unfolds like an invitation to hum, and so Jarrett does.