But he was the respected patriarch of a blue-blood political dynasty - son George spent eight years in the White House, and son Jeb served as governor of Florida.
The office of former President Barack Obama and Michelle Obama said Bush's life was "a testament to the notion that public service is a noble, joyous calling".
The cartoonist who memorialized the Barbara Bush after her death discussed his latest cartoon, which honors George H.W. Bush, Saturday on Fox & Friends.
"A new breeze is blowing and a world refreshed by freedom seems reborn", President Bush said.
The Trumps said: "With sound judgement, common sense and unflappable leadership, President Bush guided our nation and the world to a peaceful and victorious conclusion of the Cold War".
Democratic political strategist Donna Brazile tweeted: "President George H.W. Bush was the real deal. If you're looking for a role model, I told my children when they were growing up, start with George Bush".
"As president, he set the stage for the decades of prosperity that have followed". Consider that a Bush was on the ballot in every presidential election but one from 1980 to 2004.
Bush died on Friday, US time, at the age of 94. Shot down over the Pacific by Japanese anti-aircraft fire, he parachuted out and was rescued by a submarine after huddling in a life raft for four hours while enemy forces circled.
As a younger man he served in the US Army during the Second World War, and was considered a war hero by many.
He then graduated from Yale University, and launched a brief career in the oil industry. Twenty months later, in 1992, the Republican Bush lost his bid for re-election to Democrat Bill Clinton, whose folksy manner and focus on the economy struck a chord with many Americans and made Bush seem disconnected from voters for focusing on foreign policy over domestic issues.
The 43rd president of the United States and Mr Bush's eldest child, George W Bush, released a statement through family spokesman Jim McGrath.
The World War veteran and former Central Intelligence Agency director was sworn into office in 1988 after eight years as Ronald Reagan's vice president.
"The world mourns the loss of a great American".
The Dalai Lama, offered condolences to Bush's son, George W. Bush, who later became president from 2001 to 2009.