"It was a recent decision," says a source close to the couple. "She's been holding out hope but she has to look out for herself."
TMZ reports the divorce filing will happen Friday.
Although divorce at times seemed "unavoidable," Kardashian and Odom, who wed in September of 2009, had been trying to work through recent problems stemming from Odom's past drug abuse and other issues.
In November, a source told PEOPLE they "have been going to couples therapy." Things looked hopeful for the pair when Odom joined Kardashian's family at Kanye West's concert on Oct. 28.
But despite her best efforts, the source says of Kardashian, "She realized it's the best thing to move on."
On Wednesday, she was seen at the Hollywood Reporter's Women In Entertainment breakfast at the Beverly Hilton without her wedding ring. The source adds that not wearing her ring in public – or in private – "says a lot."