"The former president is awake and alert, and not in any discomfort," Jim McGrath said on Twitter.
The 41st president will likely remain at Southern Maine Health Care, in the state of Maine, under observation for a few days, McGrath wrote.
Bush, 93, spent more than a week at a Houston, Texas, hospital in late April and early May, immediately after the funeral of his beloved wife Barbara Bush.
At that time, Bush contracted an infection that spread to his blood and initially left him in intensive care.
Bush is the father of George W. Bush, who served as president from 2001 to 2009.
The elder Bush was elected president in 1988 but served only one term, going down to defeat against Democrat Clinton in 1992.
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