"I'm humbled and overwhelmed by the support we've received across the district," Sanford said in a statement. "I've always said that this race is not about people, it's about ideas -- but the ideas being advanced by myself and my opponent in this general election that starts right now couldn't be more at odds with one another."
Sanford received 57 percent of the vote in the contest with Curtis Bostic, a conservative Christian and former Charleston County Council member, The Wall Street Journal reported.
The winner of Tuesday's runoff will face Democrat Elizabeth Colbert Busch in the May 7 special election, called after Rep. Tim Scott, a Republican, was appointed to the Senate to replace Jim DeMint, who resigned to lead the Heritage Foundation.
Republican presidential nominee Mitt Romney won 57 percent of the votes in 2012 in South Carolina's 1st Congressional District.
Sanford, 52, was a two-term governor when in June 2009, after saying he was going hiking on the Appalachian Trail, he publicly revealed he had engaged in an affair with Maria Belen Chapur, an Argentine woman. He was censured by the state General Assembly following an ethics investigation into allegations he misused state travel funds to conduct his affair but avoided impeachment.
Notable deaths of 2014 [PHOTOS]