Kidman arrived at Tuesday's première with director Amenabar
A week ago a Los Angeles Superior Court judge signed the papers allowing the fast-track divorce to proceed on Wednesday.
Now attention will move to the value of the divorce settlement, which may be the largest that Hollywood has yet seen.
Tom Cruise's fortune is reported to be in the region of $250m, and includes five houses, two aeroplanes and around $1m worth of jewellery.
The couple must reach a private settlement before October to avoid a court battle over the fortune.
California law
The result could be expensive for Cruise.
If it is proved that the couple were really together for 10 years or more, California law states that the assets of the marriage be divided equally.
That could mean a settlement even greater than the $100m that Amy Irving took with her after her divorce from Steven Spielberg with in 1989.
Tom Cruise's lawyer Dennis Wasser told the BBC: "He will provide what is required by law and as I have said many times this means Miss Kidman will leave the marriage with tens of millions of dollars."
Cruise was reluctant to comment when he appeared at the première of The Others, a film he made with Kidman, in Los Angeles on Tuesday evening.
Première
"It's over, we're moving forward with our lives and I think it's important for people to mind their own business," Cruise told reporters.
Kidman arrived for the première with actresses Naomi Watts and Rebecca Rigg, and the film's director Alejandro Amenabar.
She spent several minutes signing autographs before entering the Directors' Guild of America's screening auditorium.
Cruise arrived about 20 minutes later, and the two did not see each other on their way into the screening.
The film, produced by Cruise, stars Kidman as a God-fearing mother trying to take care of her two children inside a haunted house.
Cruise and Kidman, who have two adopted children, Isabella, 8, and Conor, 6, ended their 10-year marriage in February.
Cruise filed for divorce, claiming "irreconcilable differences".
However, Kidman said in a recent interview that she refused to allow the break-up to make her bitter.
"I still completely believe in love and I remain open to anything that will happen to me," she said.