The cover art, designed by Andy Votel, is a collage loosely based on Leonardo da Vinci's drawing Vitruvian Man. For the American release of the album, the album's cover was altered to remove a photograph of American actor and director Woody Allen, which was unauthorized by the copyright owners of the photograph. In addition, the song "Magic in the Air" was re-recorded with new instrumental parts to replace a section of the song utilizing lyrics taken from the 1987 song "Love Is Contagious" by R&B singer Taja Sevelle, after Sevelle's publishing company BMG objected to the use of the lyrics.
The Hour of Bewilderbeast was widely acclaimed by music critics. On the review aggregate site Metacritic, the album holds a score of 78 out of 100, indicating "generally favorable reviews." Michael Hubbard of musicOMH felt that the album "deserves to do well for many more reasons than the act's name, excellent though it is", and that "a surprise is set loose with every track". Calling the album a "concise tour through the gentler side of British songwriting history", Brent DiCrescenzo of Pitchfork wrote that the varied instrumentation " insect wings to the lovely songs" and concluded that with The Hour of Bewilderbeast, "Badly Drawn Boy proves what shallow saps American liberal arts majors can be behind a guitar." AllMusic's John Bush stated that Gough had written and produced "over a dozen excellent songs of baroque folk-pop for his album debut, and the many gems can't help but shine through all the self-indulgence", highlighting Gough's use of humour in his lyrics.
Alternative Press stated that The Hour of Bewilderbeast gives "as full a portrait as possible of Gough's musical and personal life," while David Browne, writing in Entertainment Weekly, called the album an "intimate hour that's far from bewildering." Pat Blashill of Rolling Stone compared Gough to Elliott Smith and Nick Drake and wrote that "like Drake, he's mastered the art of evoking melancholy without slathering on too much sentimentality." Robert Hilburn of the Los Angeles Times drew similar comparisons to Drake, while noting that Gough "never succumbs to Drake's sad solipsism, though, favoring an expansive reach emotionally and musically." In a more mixed assessment, Spin's Barney Hoskyns wrote that "Gough's dewy little tunes are mere scribblings in the margins of alt-folk's dog-eared hook-book, while his too-cool-to-care singing is drip-dry dreary" and that The Hour of Bewilderbeast, when compared to Elliott Smith's Figure 8, makes Gough "look like an imposter."
The Hour of Bewilderbeast appeared on several year-end lists. Pitchfork ranked the album at number 18 on its list of the top 20 albums of 2000. NME ranked the album at number 4 on its list of the 50 best albums of 2000. In addition, the album received the 2000 Mercury Prize, a prize Gough was favoured to win. When Gough received the prize, he tossed the prize money on the ground and said: "I always assumed I was never going to win because good things don't happen to good people normally."
The album was also listed in the book 1001 Albums You Must Hear Before You Die.