Just before the release of the album, it was reported that singer Jay Kay's love of sportscars had reached a peak, and as such was reflected by the album cover which resembled the Ferrari logo as well as the engine noises on the title track. The title track, "Travelling Without Moving" appropriately introduces a new high-octane sound which features strongly in later albums. The RIAA certified Travelling Without Moving Platinum on 3 November 1997, denoting 1 million shipments in the United States – this is the only RIAA certification the band has ever obtained. The name of the album seems to be a reference to the film Dune, which includes the line "Travelling without moving" in its intro sequence.
Q gave the album 4 out of 5: "Tighter and more compact in its production than the epic funk arrangements of... The Return of the Space Cowboy… No-one with ears can deny Jason Kay's musicality — he's an extraordinary singer, and proves it here." The Source also gave the album 4 out of 5: "Travelling is essentially about the metaphysics of having a good time… Jamiroquai have a thousand musical tricks up their sleeves; edgy horns laced with jazz intricacies, energetic bass lines and disco rhythms."
Sales were helped by the success of "Virtual Insanity", which won a Grammy Award and four MTV Awards. The album went triple platinum album in the United Kingdom, and was certified platinum by the RIAA in the United States. With the success of Travelling Without Moving, Jamiroquai's popularity had increased considerably and influenced fans to listen to past releases. "Virtual Insanity" became one of the first songs by Jamiroquai to reach America, and subsequently made the band a household name.
"If I'm not mistaken," noted Jay Kay as 1997 closed, "Travelling Without Moving has now sold well over five-and-a-half million worldwide, with a million-and-a-half here and another million in America. Cleaned up at the American MTV awards and just come back from supporting The Rolling Stones over there. In fact, we even met Jack Nicholson backstage in Las Vegas the other night. He said he loved the show, which was nice."
"Virtual Insanity" is a playable song on the karaoke game for Xbox 360, Lips. "Cosmic Girl" appears in the European version of the GameCube game Donkey Konga, as well as the Wii game Just Dance 2. "Cosmic Girl" was also used in the 2000 film Center Stage. "Use The Force" was used in the 1998 film Sliding Doors. "Travelling Without Moving" is used in the introduction video to the PlayStation game Speed Freaks. References to popular science fiction and space travel concepts are found in the album's title and several songs (e.g. in the film Dune, the technique used by the Guild Navigators to fold space is referred to as "travelling without moving"). "Cosmic Girl" contains references to Star Trek, Barbarella, hyperspace, transporters, and "close encounters". "Alright" contains references to Islands in the Sky and "Use the Force" contains references to Star Wars.