Bush was admitted to Houston Methodist Hospital falling ill recently.
"He's there. He's fine and he's doing really well," Bush's chief of staff, Jean Becker was quoted as saying by Houston Chronicle newspaper.
She said the doctors have a couple of theories about Bush's condition, but he is responding to treatment.
Becker did not specify the reason why Bush was hospitalised.
Bush, who lives in Houston, Texas, is expected to be discharged in the next couple of days, the report said.
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As is the case with most people his age, Bush has had his share of health issues in recent years.
In July 2015, he was taken to a hospital in Portland, Maine, after he fractured a bone in his neck in a fall at the family's summer home in Kennebunkport. He was "up and talking and out of bed" within a day after the fall.
The fall happened about six months after he was taken by ambulance to Houston Methodist for what his spokesman called "shortness of breath." He was released from the hospital about a week later.