Trump tweeted his statement from Buenos Aires, where he arrived on Thursday for the G20 summit.
Bush had one of the most impressive résumés in American public life.
The longest living president in United States history, one of his biggest achievements was steering America through the end of the Cold War.
"George HW Bush was a man of the highest character and the best dad a son or daughter could ask for", he added.
He was the 41st USA president between 1989 and 1993, after serving two terms as vice-president to Ronald Reagan.
Bush presided over economic malaise at home, and infuriated his fellow Republicans during a budget battle with rival Democrats by famously breaking his vow: "Read my Lips: No new taxes".
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In April, he was admitted to a hospital intensive care unit with a blood infection, a week after the death of his wife of 73 years, Barbara.
Bush was hospitalized in January 2017 for pneumonia, at which time they had to insert a breathing tube.
In late 1989, Bush sent U.S. troops to Panama to oust strongman Manuel Noriega.
During his four years in the White House, Bush ordered a military operation in Panama to overthrow its drug-trafficking leader, Manuel Noriega.
Bush faced a serious challenge when Iraqi President Saddam Hussein invaded Kuwait in 1990. Bush pulled in only 168 electoral votes that year, compared to Bill Clinton - then the governor of Arkansas - who collected 370 electoral votes. Bush oversaw the opening of his presidential library in College Station, Texas, and was widely honored as an elder statesman.
Mr Bush was the longest-lived president in United States history with no other president having lived as long. "But I see history as a book with many pages, and each day we fill a page with acts of hopefulness and meaning".