"Mr. Bush has improved to the point that he will not need any special medication when he goes home, but he will continue physical therapy," Dr. Amy Mynderse told the Houston Chronicle.
Bush said in a statement he was grateful to the doctors at Methodist Hospital for the care he received and touched by the many get-well messages he received from friends and well-wishers.
"As I head home my only concern is that I will not be able to thank each of you for your kind words," Bush said.
Visitors said Bush was in a good mood and joking with family members and hospital staff and that he was "looking forward to heading home," NBC News said.
Bush, 88, was admitted to the hospital Nov. 29, suffering from severe bronchitis. He was in intensive care in December because doctors had difficulty controlling a fever that developed after the cough.
Sources close to the former president indicated last week his condition had improved.
Bush was elected president of the United States in 1988 and is the country's oldest living president.