Speaker, 31, an Atlanta attorney, left Denver in an air ambulance and is now at an undisclosed location in Georgia to recuperate, said William Allstetter, a spokesman for National Jewish Medical and Research Center.
Allstetter said Speaker is not in a hospital but he would not provide any other details.
"He arrived there safely, and he is happy to be home," Allstetter said.
Speaker has multidrug-resistant TB. Officials at the Centers for Disease Control and Prevention initially thought he had extensively drug-resistant tuberculosis, or XDR-TB, which is much more difficult to treat.
Speaker will continue antibiotic treatment for about two years, the hospital said.
The doctors who treated him at National Jewish don't consider him to be completely cured, but a lung operation and antibiotic treatments "have eliminated any detectable evidence of infection," the hospital said.
He had been at National Jewish since May 31.
Speaker is not contagious and could have flown by commercial airliner, but "everyone involved in the case" decided the air ambulance was a better choice because of the attention the case has attracted, the hospital said.