Scott will serve for two years and then face an election in November 2014. That would give South Carolina two Senate elections: one for Scott and the other for two-term Republican Sen. Lindsey Graham.
"I have no doubt he'll fly through 2014," Haley said of Scott.
Scott said he still believes in term limits and would likely limit himself to two terms in the Senate, starting with 2014.
After asking for a moment of silence for the victims of the Connecticut school shooting, Scott said he accepted the challenge of trying to help the country through troubling times.
"Our nation finds itself in a situation we need backbone. We need to make some very difficult decisions," Scott said. "I learned early in my 20s that if you have a problem with spending, there's not enough revenue to make up for it. We have a spending problem in America."
Scott grew up in poverty in North Charleston. His parents divorced when he was 7, and he remembered his mom working 16 hours a day to support him and his brother.
"To the single moms out there, don't give up on your kids. It may get tough. It may be challenging, but all things are truly possible," he said.
In high school, he said he was failing four courses and in danger of "flunking out of high school" until he met the late John Moniz, a conservative entrepreneur who ran a Chick-fil-A beside the movie theater where Scott worked.
They became friends and Scott said Moniz taught him important values and basic business principles.
Scott earned a degree in political science from Charleston Southern University, which is affiliated with the South Carolina Baptist Convention and touts how it integrates faith into learning and serving.
Graham, South Carolina's senior senator, said Scott has a unique opportunity to inspire others and be a leading voice for the conservative cause.
"When it comes to trying to explain what America's all about, I could not tell a better story than the story of Tim Scott," Graham said. "Tim is what America's all about."
The governor won't name a replacement for Scott. By state law, U.S. House vacancies are filled through a special election.
Associated Press Writer Donna Cassata in Washington contributed to this report.