The mission is planned for late 2018, SpaceX CEO Elon Musk said, adding that the tourists "have already paid a significant deposit".
"This presents an opportunity for humans to return to deep space for the first time in 45 years," he said.
The two unnamed people will fly aboard a spaceship which is set for its first unmanned test flight later this year.
Mr Musk said the co-operation of America's Nasa space agency had made the plan possible.
He said the two passengers "will travel faster and further into the solar system than any before them".
Mr Musk declined to reveal their identities, only saying that they knew each other and that "it's nobody from Hollywood".
"Like the Apollo astronauts before them, these individuals will travel into space carrying the hopes and dreams of all humankind, driven by the universal human spirit of exploration.
"We expect to conduct health and fitness tests, as well as begin initial training later this year."