Early returns showed the former first lady gaining roughly half the vote in a three-way Democratic race, with Obama at about 45 per cent and John Edwards placing a distant third.
'Votes for change'
Romney said Republicans had cast their votes for change, and that he was the man to provide it.
"With a career spent turning around businesses, creating jobs and imposing fiscal discipline, I am ready to get my hands on Washington and turn it inside out," Romney said in a statement.

The former governor of Massachusetts issued while he flew to Florida to campaign for that state's primary on January 29.
With about 40 per cent of the vote counted already, Romney was gaining more than half the vote in Nevada, leaving McCain and the Ron Paul in a close race for a distant second place.

However Al Jazeera's Kimberly Halkett in South Carolina said many political analysts would not place too much emphasis on Romney's victory given that many of the other candidates did not campaign heavily in Nevada preferring to focus on South Carolina.

In the Democrat race Obama had seen his hopes boosted by support from the Culinary Workers Union, which endorsed him last week.

But it appeared that turnout was lighter than expected at nine caucus sites established along the Las Vegas Strip for the union membership.