"Sometimes relationships just run their course," an unnamed source close to the couple told the New York Post, confirming the split.
The Oscar winner and country music hit-maker have been living apart since June, according to entertainment website TMZ.
In June, Kidman, 58, shared a photo of herself cuddled up to Urban on Instagram to celebrate their wedding anniversary.
Four-time Grammy winner Urban, 57, has moved out of the couple's Nashville home, according to the reports, amid claims Kidman is desperate to save the relationship.
"She didn't want this," another unnamed source told People magazine.
"She has been fighting to save the marriage."
On Tuesday, after the split was revealed, Urban's last post on his Instagram, made in February, suddenly began filling up with new posts from followers pleading with him to save his marriage.
The couple share two children, Sunday Rose, 17, and Faith Margaret, 14.
Kidman last posted on her Instagram a week ago, when she attended the Nashville Film Festival.
While both parties are yet to confirm the split, it isn't the first time the pair has separated.
Just months after they married, Urban, a recovering alcoholic and drug user, fell off the wagon - and they spent some time apart before reuniting.
The couple have said they had a pact never to spend more than two weeks apart, which meant if both were working abroad they would come together for at least one night.
Eyebrows were raised in July when an online interview with an Adelaide radio show abruptly ended after Urban was asked how he felt about his wife's intimate scenes with Zac Efron in the movie A Family Affair.
It's unclear whether Urban or his team ended the call or if the call dropped out due to a technical issue.
In January, Urban thanked Kidman - affectionately calling her "Nicole Mary" - while being inducted into the Roll of Renown at the Golden Guitar country music awards in Tamworth.
Kidman was unable to watch him accept the Australian country music honour because she was filming in Nashville and Germany, he said.
"I want to thank our girls, Sunday and Faith," he said during his acceptance speech.
"I couldn't be here without the three of them and their love."
Richard Wilkins, Nine's long-time entertainment editor, declined to comment directly on the news, citing personal confidentiality.
"They're both very treasured friends of mine, and I love them both very dearly," Wilkins told the Today program.
"I have nothing to add to this story. They've never commented on any of my circumstances over the years and I'm not going to comment on theirs.
"Nineteen years ... I mean we're talking about Hollywood, that's got to be like 50, 60 years."
Kidman is believed to have just wrapped on the Practical Magic sequel, and is set to star in the Amazon series Scarpetta alongside Jamie Lee Curtis, as well as the HBO series The Last Anniversary.
The second season of Nine Perfect Strangers is also expected to premiere later this year.
The Babygirl actress reportedly applied for Portuguese residency earlier this year.
The couple married in June 2006, after meeting at the G'Day USA gala in January 2005.
Kidman was previously married to Tom Cruise from 1990 to 2001. She and the Top Gun actor share two adopted children, daughter Bella, 32, and son Connor, 30.
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