Bush is expected to lie in state in the US Capitol.
The Obamas credited him with "expanding America's promise to new immigrants and people with disabilities".
Despite achieving popularity ratings of 90%, Bush was accused of neglecting domestic affairs and was defeated by Bill Clinton in the 1992 election.
Born in Milton, Massachusetts on June 12, 1924, he enlisted in the armed forces on his 18th birthday.
In 1944, Bush survived a Japanese hit while flying a torpedo bomber over the western Pacific.
Bush was married for 73 years to the former Barbara Pierce, a woman he met in his teenage years.
Microsoft briefly ousts Apple as the most valuable company
Below is a chart comparing the market caps of Apple (NASDAQ: AAPL ) and Microsoft (NASDAQ: MSFT ) going back to 1986. However, by the stock market's close, Apple was able to regain the spot with a market value of over $825 billion.
After a 1989 explosion on the USS Iowa killed 47 crewmen, Bush delivered a speech in which the emotional high point was meant to be a line in which he talked about his own experience taking off in the morning and coming back to an empty deck. He had come to know many foreign leaders through his service as vice president, Central Intelligence Agency director, ambassador to the United Nations and envoy to China.
He and Barbara then moved to Texas where he worked in the oil business and was elected to two terms in the U.S. House of Representatives.
The Bushes had been regular fixtures in their adopted hometown of Houston after his presidency, but public appearances became more rare because of health problems as they reached their 90s.
Though Bush lacked his predecessor's populist touch and gift for a glib phrase, in leadership he favoured behind-the-scenes consensus building and careful and considered preparation.
During his four years in the White House, Bush ordered a military operation in Panama to overthrow its drug-trafficking leader, Manuel Noriega. "We would have been forced to occupy Baghdad and, in effect, rule Iraq".
"When we are successful - and we will be - we have a real chance at this new world order, an order in which a credible United Nations can use its peacekeeping role to fulfill the promise and vision of the UN's founders".
Angela Merkel's plane makes emergency landing
German government planes, operated by the country's air force, have been plagued by technical problems in recent years. A senior journalist with the public national television ZDF said Merkel would spend Thursday night in Bonn.
Our thoughts are with George's family and friends during this hard time.
He lost his bid for re-election to Bill Clinton in a campaign in which businessman H. Ross Perot took nearly 19 percent of the vote as an independent candidate.
Bush received several accolades after his presidency, including receiving a knighthood at Buckingham Palace, and having the US Navy's nuclear-powered aircraft carrier, the USS George H.W. Bush (CVN 77), named after him.
As these images make clear, the future President whose "wit, stamina and enthusiasm" impressed the worldwide community had no shortage of enthusiasm for the rest of life as well.
His son, George W Bush, became the 43rd president of the United States.
Feds catch convicted murderer in migrant caravan: DHS
Then on Sunday, a group of the migrants attempted to cross into the USA near the San Ysidro Port of Entry. Homeland Security said he and the two men he was caught with are being processed for deportation.