As well as contributing some new songs to the soundtrack, he will have a walk-on part in the film, directed by The English Patient's Anthony Minghella.
White, a film buff whose song The Union Forever featured dialogue from Orson Welles' film Citizen Kane, recently admitted he is fascinated by the art of writing film music and the composers of classic musicals.
"When songwriters back then were writing songs for a musical, they had a job to do," he said.
"In order to get paid they had to get these melodies across. It's very hard to sit down and say, 'I'm going to write a catchy song.' I think that job is really interesting."
Cold Mountain, based on a novel by Charles Frazier, features Law as a wounded Confederate soldier who journeys from hospital to his North Carolina home to be reunited with the love of his life (Kidman).
Natalie Portman and Renée Zellweger co-star in the film, which has just begun filming in Romania and is due for release in 2003.
Meanwhile, White and his fellow band member Meg White, who hit the charts earlier in the year with Fell In Love With A Girl, have just finished recording their fourth album, tentatively titled Elephant, in East London.
They are due to return to the States to play shows in New York and Detroit with The Strokes, with each band headlining its home city.
The duo will also appear at the Carling weekend festivals in Reading and Leeds later this summer.