Kidman stars in Moulin Rouge with Ewan McGregor
Williams invited the actress to sing with him on Swing When You're Winning - his Sinatra tribute album - but was surprised she agreed.
"I heard her sing in Moulin Rouge and I asked if she would be interested and fully expected to be knocked back - she is a proper Hollywood star," Williams said.
"But she said yes - I was amazed and thrilled."
Kidman said she had fun making the recording of Something Stupid, which only took an afternoon's work.
But she added that she has no intentions of changing her career.
"I have no desire to be a singer," she said.
"I just did that for fun."
The actress, who wowed London with her stage performance in The Blue Room, said that William's version of Mr Bojangles made her cry.
And less than a month after her divorce from Tom Cruise, she flirtatiously commented on Williams charms.
"He is a total pleasure to work with. He put me at my ease and made me laugh.
"Now I am seriously thinking of getting a tattoo like his," she said, tongue firmly in cheek.
Williams has a Maori tattoo on his upper arm.
Since he left boy band Take That 10 years ago, Williams has established himself as one of the brightest solo stars around.
He stormed the British charts with his third album, Sing When You're Winning, which included the singles Rock DJ, Supreme and a duet with Kylie Minogue on Kids.
Rock DJ won him two of his three Brits in 2001 - for best British single and best British video, as voted for by fans.
He sees the tribute album, recorded in Los Angeles with the same band that backed Sinatra, as a privilege.
Williams said of the recording: "I've loved this music since I was a kid and for me to sing in front of the band that backed Frank Sinatra in the same studio that he used is an absolute honour."
Bill Miller, the venerable pianist who played on Sinatra's original One For My baby, accompanied Williams on the same song.
"This is the most fun I have ever had recording," said Williams.