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Bush was admitted to Southern Maine Healthcare Hospital for fatigue and low blood pressure on May 27.
Spokesman Jim McGrath tweeted that "the president is deeply appreciative both for the terrific care and the many good wishes he has received."
Bush entered the hospital a little more than a month after his wife and former first lady Barbara Bush died and weeks after he was discharged from a Houston hospital.
He and his family are in Kennebunkport, Maine, where they have traditionally spent the summer. He has been in Maine every summer of his life, except the years he spent fighting in World War II.
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He arrived this year on May 20.
WATCH: An update on George H.W. Bush's condition
Neighbors express words of hope as former President Bush recovers