DeMint didn't respond to an interview request from the Associated Press.
His job with the foundation starts Jan. 3, but DeMint won't officially become president until April 3, when founder Edwin Feulner retires, said foundation spokesman Jim Weidman.
DeMint's resignation comes a day after the foundation board voted to make DeMint the next president. The senator began talking with the committee that was choosing Feulner's replacement several months ago, Weidman said.
Republican Gov. Nikki Haley will appoint DeMint's Senate successor. She told a Greenville talk-radio station she plans to pick someone who will fight for conservative ideas. She said she wouldn't let the process drag out. Haley didn't specify anyone she favored to replace him, but did take one name out of contention.
"I will not be appointing myself. That's not even an option," Haley told WORD-FM.
DeMint's former state director, Luke Byars, said the senator's new role will allow him to effect change outside the U.S. Capitol. In the fall election, Democrats strengthened their majority in the Senate.
DeMint, who previously ran a marketing firm, thought conservatives didn't do a good job communicating their message in the presidential race, Byars said.
"He knows how to communicate," said Byars, a political consultant. "This is a vehicle for him to push and pull on conservative issues on a national stage, to get the attention of folks inside Washington."
The resignation will have a ripple effect on the state GOP leadership. Whomever Haley appoints would face a special election in 2014 to finish DeMint's term, which expires in 2016. Sen. Lindsey Graham, DeMint's Republican colleague from the state, faces reelection in 2014.