The Second World War hero, who also presided during the collapse of the Soviet Union and the final months of the Cold War, died shortly after 10pm on Friday, family spokesman Jim McGrath said.
Tributes have poured in from across the globe from politicians.
The White House released the statement that read: "Through his essential authenticity, disarming wit, and unwavering commitment to faith, family, and country, President Bush inspired generations of his fellow Americans to public service - to be, in his words, 'a thousand points of light' illuminating the greatness, hope, and opportunity of America to the world."
Prime Minister Theresa May said: "President George HW Bush's ethos of public service was the guiding thread of his life and an example to us all."
Sir John Major has also paid tribute to President George who he described as a "lifelong friend".
"In public office he served as he lived, with compassion, courage, dignity and grace," he said.
His wife of more than 70 years, Barbara Bush, died in April.
Mr Bush's son, George W Bush, described his father as a "man of the highest character and the best dad a son or daughter could ask for".
In a statement, he added: "The entire Bush family is deeply grateful for 41's life and love, for the compassion of those who have cared and prayed for Dad, and for the condolences of our friends and fellow citizens."
He was elected as the 41st President in 1988 and served a single term before losing his 1992 re-election bid to Democrat Bill Clinton.
Months into his presidency he was faced with the dissolution of the Soviet Union and he oversaw the removal of Panamanian dictator Manuel Noriega.
In August 1990 he responded to Saddam Hussein's invasion of Kuwait, creating a national coalition led by the US that liberated the oil-rich yet tiny nation but stopped short of toppling the Iraqi dictator.
But it was during the presidency of his son, George W Bush, that Saddam's rule eventually ended.
In his later years he developed a form of Parkinson's disease and used a motorised scooter or a wheelchair for mobility.
Bush was admitted to hospital in Maine in 2015 after falling at his summer home and breaking a bone in his neck.
He was taken to hospital the previous December because of shortness of breath and spent Christmas 2012 in intensive care for a bronchitis-related cough and other issues.
Despite the loss of mobility, Bush celebrated his 90th birthday by taking part in a tandem parachute jump in Kennebunkport, Maine.
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