A family spokesman said the nation's 41st president died shortly after 10 p.m. Friday, local time, eight months after the death of his beloved wife, Barbara.
Bush senior served from 1989 to 1993, and eight years later watched his son George W. became the 43rd president.
The elder Bush saw his popularity swell with the United States' success in the Gulf War in 1991, only to watch it evaporate in a brief but deep recession.
The Republican was defeated in his bid for a second term by Democrat Bill Clinton.
Bush had also been a World War II hero, Texas congressman, CIA director and Ronald Reagan's vice president.
The 41st president had been admitted to hospital following the death of his wife Barbara.
"Jeb, Neil, Marvin, Doro and I are saddened to announce that after 94 remarkable years, our dear Dad has died," his son, former president George W. Bush, said in a statement released on Twitter.
The former Republican Party stalwart had a form of Parkinson's disease and a history of pneumonia and other infections.
He will go down in history as the president in charge at the end of the Cold War who took the United States into the first Gulf conflict.
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.
It was during the presidency of his son, George W Bush, that Saddam's rule would eventually end.
Bush Snr, a Second World War veteran, was born George Herbert Walker Bush in Milton, Massachusetts, on June 12 1924.
He enlisted on his 18th birthday and was the youngest pilot in the US Navy when he received his wings and went on to fly 58 combat missions.
One saw him shot down by Japanese anti-aircraft fire over the Pacific, leaving him to be rescued by a US submarine.
He was later awarded the Distinguished Flying Cross for bravery in action.
In January 1945 he married Barbara Pierce, with whom he went on to have six children – George, Robin (who died as a child), John (also known as Jeb), Neil, Marvin, and Dorothy.
His political career saw him occupy a number of positions including congressman, CIA director and Ronald Reagan's vice president for the Republican Party before becoming the first member of the Bush political family to reach the nation's top office.
George W Bush would go on to be elected president in 2000 after Mr Clinton and served two terms.
Another son, Jeb – a former Florida governor – made an unsuccessful bid for the Republican nomination in 2016.
Only one other US president, John Adams, had a son who also became president.
In 2011, Bush was honoured with the Presidential Medal of Freedom by President Barack Obama.
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