George W Bush, who was the 43rd president, issued a statement following his father's death.
"Jeb, Neil, Marvin, Doro and I are saddened to announce that after 94 remarkable years, our dear dad has died", he said.
President Donald Trump said George HW Bush "set the stage for the decades of prosperity" following his years in power.
"The entire Bush family is deeply grateful for 41's life and love, for the compassion of those who have care and prayed for Dad, and for the condolences of our friends and fellow citizens".
The decorated war pilot and former Central Intelligence Agency chief suffered the ignominy of being a one-term president, denied a second term over a weak economy when he lost the 1992 election to upstart Democrat Bill Clinton. In 1945 he had married Barbara Pierce and the couple went on to have six children, though their daughter, Robin, died in 1953 of leukemia when she was four years old.
It was there that Bush became involved in politics, first losing a U.S. Senate race in 1964 before winning election to the U.S. House of Representatives in 1966.
Remarkably, Bush developed a late passion for skydiving, jumping to celebrate his 85th birthday in 2009 and the opening of his presidential library in 2007.
"The state of Texas mourns with the nation at the passing of one of our greatest Presidents".
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Mrs Bush died in April 2018. "His life spanned the American Century - he fought in World War II ... took part in the Texas oil boom ... served out a distinguished career in public service including serving as president during the final days of the cold war".
The elder Mr Bush, the son of a senator, rose through the political ranks: from congressman to United Nations ambassador, Republican Party chairman to envoy to China, CIA director to two-term vice president under the hugely popular Ronald Reagan. He carried 40 states and achieved a almost 7 million-vote plurality, becoming the first sitting vice president to be elected president since Martin Van Buren in 1836.
Bush served as Vice President to Ronald Reagan in the 1980s, and in 1988 won the Republican nomination for president.
The longest living president in USA history, one of his biggest achievements was steering America through the end of the Cold War. "But I see history as a book with many pages, and each day we fill a page with acts of hopefulness and meaning".
After two terms and another failed Senate bid in 1970, he was appointed by President Richard Nixon as USA ambassador to the United Nations.
Bush did not endorse fellow Republican Trump, the eventual victor of the 2016 presidential election, who attacked both Jeb and George W. Bush during his campaign. It was the longest marriage among any US presidential couples.
The Bushes were renowned for having a happy marriage, which was underscored with gentle good humour. "Our thoughts are with the entire Bush family tonight - and all who were inspired by George and Barbara's example". A spokesman for George Snr said he apologised for any offence caused and that any inappropriate touching was "unintentional".