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".