Actress and (real) singer: Johansson's debut disc is acclaimed

Scarlett Johansson's best-known musical performance to date was her pink-wigged karaoke rendition of a Pretenders song in the film Lost In Translation. But the Hollywood actress has now released an album and it has been proclaimed by one of the music industry's toughest critics as "the coolest movie/rock crossover album in the history of celebrity cash-ins".

The New Musical Express says Johansson's "astonishing debut" of Tom Waits covers, Anywhere I Lay My Head, has succeeded where other celebrities who have attempted to break into music have so miserably failed. Proclaiming the 23-year-old an "indie icon", Johansson is pictured on the cover of the NME's latest issue holding a horned animal skull between crimson-painted fingernails.

The magazine's deputy editor, Krissi Murison, said: "When people first started talking about it, we thought it didn't sound very NME; then we got the album and it floored everybody. It's really beautiful, really unexpected, with very artful, interesting influences. A lot of people's expectations of an actress making an album are that it would be manufactured and robotic. No one expected she would sound like that – a deep baritone and quite androgynous."

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NME's glowing verdict is not universal, however. The American magazine Rolling Stone gave the album just two-and-a-half stars out of five. "Johansson's voice is unremarkable and her pitch sometimes unsteady; she's a faintly goth Marilyn Manson lost in a sonic fog", the magazine wrote. Entertainment Weekly gave the album a C grade, branding the actress's voice "expressionless".

Murison said Johansson may have more appeal in Britain than in America because her musical tastes are "quite Anglophile". Johansson, who grew up listening to Depeche Mode and Radiohead, is a fan of the Scottish bands Cocteau Twins and The Jesus and Mary Chain, with whom she sang the track "Just Like Honey" at the Coachella Festival in California last year.

Scarlett Johansson's video for single "Falling Down"

Johansson was invited to make an album by Rhino Records, the label behind last year's Led Zeppelin compilation album Mothership, which heard Johansson sing "Summertime" on a 2006 compilation of recordings by actors.

The actress, a protégée of Woody Allen, agreed to cut the CD but her first attempt at a Waits cover album was, by her own admission, a flop. It was only when she teamed up with Dave Sitek, the producer recently ranked number one in NME's list of the 50 most forward-looking people in music, that success beckoned. Sitek came up with the idea to take Johansson to a Louisiana recording studio to recapture some of the rawness of Waits' original recordings. David Bowie provides backing vocals on two of the album's tracks, and sound effects including owls and rainstorms were used. "It's Dave Sitek who opened the horizons of what this album could be and brought in ideas," said Murison.

Initially, Johansson just wanted to record "I Never Talk To Strangers", a duet between Waits and Bette Midler. Then to balance the song out, she recorded some more Waits songs until she had an entire album of covers, plus one original track, "Song For Jo", which she and Sitek co-wrote. In an interview with the NME, Johansson said she had been a fan of Waits since the age of 13, when her father played the singer's music to her and a friend. "At first we were like, 'What is this noise? Chainsaws hitting nails into walls?' But we liked it and it became our little secret, the music that we were into that none of our friends knew about," she said.

"What gripped me about it was that he writes from shadows. It's really dark and shadowy music that talks about the emotion, passion and rawness of the human condition and there's this real fire to it."

Musical interludes

Paris Hilton

Released her debut album, Paris, on Heiress records in 2006. It received a mixed critical reception.

Keanu Reeves

Bass guitarist in the rock band Dogstar, which supported Bon Jovi in 1995, before quitting in 2002 over work commitments.

Russell Crowe

Sang with 30 Odd Foot of Grunts. He quit in 2005 before returning in a new band with the same initials, The Ordinary Fear of God.

Minnie Driver

In the UK last week performing her second album, Seastories, which has just been released to warm reviews.

Bruce Willis

Released his debut album, The Return of Bruno, a collection of R&B covers with The Temptations, in 1987.

William Shatner

Recorded a spoken-word album with orchestral backing, The Transformed Man, in 1968. It included a version of Lucy In The Sky With Diamonds.