In a news release, the National Park Service said rangers had located J.R. Kimbler, his 10-year-old son, Dakota, and his 6-year-old daughter, Jade.
The three did not appear to be seriously hurt and were being taken to a local hospital for observation, officials said. Authorities planned to release more information later in the day.
Crews traveling by airplane, boat and on foot had been looking for the family in the 27,000-acre site since the father sent a text message late Saturday saying they were lost.
Officials closed the park Monday afternoon during the search. An investigative team from the National Park Service had also checked on leads outside the park in case the family members had not been lost while hiking.
There had been no indication Kimbler, 43, took any camping gear or other items for an overnight stay. The taxi driver left his cigarettes in his cab that was still parked near the visitor's center Monday, and his daughter's inhaler and other medicine were in the hotel room where he lived, according to his family.
The park has marked trails, but beyond the paths are tangles of old growth trees, swamps and underbrush. The land has become even more rugged since an ice storm in February knocked down thousands of trees and limbs.
"Many of the trails you can't see to navigate right now," said Sana Sohen, a park service spokeswoman.
The mother of the two children, Tammy Ballard, was at the park during the search, walking down trails, calling their names.
"It's been tough. I see so many footprints out there," Ballard said Monday. She did not immediately respond to a phone message Tuesday.
Officials had been worried because of the storms expected to move into the state later Tuesday.
Kimbler had been out of his children's lives for a few years but recently started to get them on the weekends, said Chris Ballard, stepbrother of the missing children.
Kimbler took them to the skating rink and the zoo in recent weeks. The trip to Congaree National Park was the first time he had been out there, he said.