According to the coming issue of the New York Times' Book Review supplement the book, which pairs the song's nonsense lyrics with illustrations by Svein Nyuhus, one of Norway's leading illustrators, is now the bestselling children's book in the US.
The book, published on December 10, and is already in its sixth printing, after it was widely tipped as a Christmas gift for children.
Christian Løchstøer, Managing Editor of Tonight with Ylvis, the brother's show is credited, along with the brothers with writing the lyrics.
The Fox topped out at Number 6 on the US charts, and has received more than 300m hits on YouTube, making it this year's most viewed video.
Bård Ylvisåker yesterday downplayed the importance of further US success to him and his brother Vegard.
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"We'll return to our office in Norway and still be happy. Everything's a bonus. And we won't be disappointed if we're kicked out of the country," he told The Hollywood Reporter.