The ceremony had been due to take place in the summer, but due to media attention Ms Smart, 24, and her fiancé Matthew Gilmour decided on the 'spur of the moment' to bring the wedding forward, according to the bride's father.
'She is positively radiant,' said a spokesman for the Smart family. 'And Matthew couldn't be happier.'
The couple, who are both Mormons, married at the LDS Laie Hawaii Temple, but plan to settle in Salt Lake City, Utah.

'Elizabeth's desire was for what most women want — to celebrate her nuptials in a private wedding with family and close friends,' said family spokesman Chris Thomas.
'After the story broke about her engagement and the media became increasingly invasive, Elizabeth recognized it was going to be impossible to have a traditional wedding devoid of distractions and unusual challenges outside of her control.

'She decided, about a week ago, the best way to avoid significant distraction was to change her wedding plans and to get married in an unscheduled ceremony outside of Utah.'
Ms Smart's father Ed, who described the wedding as 'kind of a spur of the moment thing', said: 'We're just thrilled she's married.'
The couple will now take an extended honeymoon in a secret location.

The pretty blonde hit headlines after she disappeared from her bedroom in 2002. Despite a nationwide search for the teen, she was not found for nine months.
It was only when an alert biker who had heard about her case on America's Most Wanted spotted her at a diner about 18 miles from her home.
In the nine months she was held captive by one-time itinerant street preacher Brian David Mitchell and his wife Wanda Barzee, she was continuously raped and was even married to Mitchell in a bizarre ceremony.
He was convicted of kidnapping and sexual assault and was sentenced to serve life in prison in May 2011.
Wanda Barzee was sentenced to 15 years in a Texas federal prison hospital for her role in the kidnapping of the girl.
It was revealed last month that Ms Smart had become engaged to 22-year-old Mr Gilmour, from Aberdeen in Scotland.
The pair met last year when they were both serving as Mormon missionaries in the south of France.

In December she spoke for the first time publicly about what she suffered at the hands of Mitchell, revealing horrific details about her ordeal, including how he dragged her from her bedroom to a camp in the woods where he performed the marriage and then raped her.
She said: 'He went straight from marrying me to raping me. And after that moment I couldn't feel more worthless and more degraded. It was the worse feeling I could have ever felt.'
'I kept begging him to let me go - and he wouldn't listen to me,' she told ABC.
'All I could do was scream ''No". He said, ''If you ever scream like that again, I will kill you.'

Although Miss Smart has published a book on her terrifying ordeal and spoken at the trial of Mitchell last year, this was the first time she was heard in public recounting the terrible details.
She had been invited to speak to members of the Salt Lake City Rotary Club to help promote her charity the Elizabeth Smart Foundation. It works in schools across the country with a programme radKIDS to educate children on how to protect themselves from danger.
The senior at Brigham Young University recalled being tied down with a cable on her first night and the deep sense of hopelessness that surrounded her.
She was held captive for nine months during which time she was raped daily by Mitchell, sometimes up to three or four times a day.
Miss Smart had testified at Mitchell's trial in 2010 in excruciating detail about waking up in the early hours of June 5, 2002, to the feel of a cold, jagged knife at her throat and being whisked away by the religious fanatic.

Within hours of the kidnapping, she testified, she was stripped of her favourite red pajamas, draped in white, religious robes and forced into a polygamous marriage with Mitchell.
She was tethered to a metal cable strung between two trees and subjected to near-daily rapes while being forced to use alcohol and drugs.
She described the horrific events as her 'nine months of hell.'
She recalled being forced to live homeless, dress in disguises and stay quiet or lie about her identity if ever approached by strangers or police.
Daily, her life and those of her family members were threatened by Mitchell, she said at the trial.


Read more: dailymail