The pair's all-candlelight ceremony took place just after sundown Sunday night at Sydney, Australia's Cardinal Cerretti Memorial Chapel on St. Patrick's Estate at Manly, reps for the couple confirmed to PEOPLE.
The couple kept a low-profile on Monday, emerging only to have lunch with family at a luxury waterfront hotel. Later that evening they were spotted boarding Kidman's private jet.
Though security during their wedding was high, the bride thrilled hundreds of spectators as she rolled up in a vintage Rolls-Royce and opened the car window to wave and thank the cheering throngs.
Guests at the black-tie event included Russell Crowe, Hugh Jackman, Naomi Watts and Rupert Murdoch.
Kidman's wedding party consisted of her sister Antonia, who was her maid of honor, and daughter Isabella, 13, who was her bridesmaid. Antonia's daughter, Lucia, was a flower girl. On the groom's side were Urban's brother Shane, who served as best man, and longtime buddy Marlon Holden, who produced Urban's first solo album in 1991.
Kidman wore a dress by Nicolas Ghesquiere for Balenciaga. Her father, Antony, walked her down the aisle under the dramatic glow of a spotlight. She kept her veil on throughout the ceremony, only lifting it when it came time to say the (very traditional) vows.
The flowers were white freesias, gardenias and carnations arranged by Sydney florist Saskia Havekes.
Kidman got ready at her home in Sydney's Darling Point with Isabella and son Connor, 11, and drove to Manly with her father in a white Rolls Royce. Bella and Antonia rode just ahead of them in a matching white Rolls Royce.
"It was so intense," the guest says. "When her veil was lifted, he moved right in and he grabbed her and kissed her. It was a long, passionate kiss. (Then) everything went from being quiet and elegant and intense to really loud, like we were suddenly at a soccer game. There was screaming and hollering and such excitement.
"But when Nicole and Keith looked at each other it was like they were the only two people in the room. They are so deeply in love. It was the most incredible wedding."
In lieu of gifts, guests were asked to donate to the Sydney Children's Hospital.
Both Jackman and Crowded House's Neil Finn performed at the reception, which had a "passion" theme and red color scheme – including red carnations hanging from huge chandeliers and red roses on the tables.
Later in the evening, the newlyweds released a statement: "We just want to thank everyone in Australia and around the world who have sent us their warm wishes."
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Over the next several days, wedding guests including Jackman, Watts, Isabella and Connor and Urban's parents and brother arrived Down Under for the celebration.
"I'm very excited for my friend," Watts told reporters upon her arrival. Jackman, who arrived later that day, joked, "Wedding? What wedding?"
Kidman and Urban's openness about their nuptials was unusual for the normally fiercely private stars. But the couple have taken the spotlight in stride, even sending cold beer on Tuesday to the paparazzi camped outside Kidman's home. On the case of 24 bottles of Victoria Bitter beer was a note: "Enjoy! Nicole & Keith."
Kidman first confirmed the couple's engagement to PEOPLE in May, saying that Urban was not just her boyfriend – "he's actually my fiancé." She added, "He's very good to me."
Kidman, 39 and Urban, 38, met in January 2005 at a gala dinner in Los Angeles honoring noted Australians. (Kidman was born in Hawaii and Urban in New Zealand, but both were raised in Australia.) By summer, they'd begun a low-profile courtship.
In July, PEOPLE reported that they'd gone on a motorcycle ride in Woodstock, N.Y., and had lunch at Elijah's Cafe, a natural-foods restaurant. In September, they spent time together in Litchfield County, Conn., dining in the garden of the Good News Cafe in Woodbury. "They looked very together," said one onlooker.
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In November, Kidman was photographed wearing a diamond on her ring finger while walking arm-in-arm with Urban in Boston. Of a rumored engagement, Urban's rep, Paul Freundlich, said at the time, "Right now it's just a rumor. When and if there's a statement, we'll make that public."
That month, the couple – and their parents – spent Thanksgiving at Urban's mansion in Nashville's posh Green Hills neighborhood.
They spent the early part of this year nesting in Nashville, dining out with neighbor LeAnn Rimes and hanging out at the local Starbucks.
"They're very loving together," a Nashville source told PEOPLE in April. "They're very doting. He holds her hand the whole time and pats the top of her other hand at the same time. It's adorable."
Said a source close to Kidman, "They seem great together. Real love just happens. You don't plan it. And that's what happened with them. They fell in love."
This is the first marriage for Urban and the second for Kidman, who was married to Tom Cruise from 1990 to 2001.