"Yes, Elizabeth did get married today and we are all thrilled," said Smart's father, Ed, on Saturday.
Smart and Matthew Gilmour exchanged vows Saturday on Oahu's North Shore before family and friends, CNN affiliate KSL said, citing a family spokesman.
They plan to honeymoon at an undisclosed location, according to Chris Thomas, the spokesman.
"Elizabeth's desire was for what most women want — to celebrate her nuptials in a private wedding with family and close friends," Thomas told the affiliate.
The pair got engaged last month and planned to get married in the summer, but moved up the wedding because of the media attention, the spokesman said.
Smart made headlines in 2002 when she was kidnapped from her Salt Lake home at age 14 and held captive for nine months. Her kidnapping stunned the nation, and the media covered the monthslong search to find her.
Her abductor, Brian David Mitchell, sexually abused her during her time in captivity, and is serving life in prison for the kidnapping and assault.
Authorities rescued Smart when she, her captor and his wife were spotted wandering in Sandy, Utah, in March 2003.
Smart described the ordeal as "my nine months in hell" during court testimony two years ago.