He said he and Melania "join with a grieving nation to mourn the loss of former President George HW Bush".
Bush served as the 41st president of the United States from 1989 to 1993.
In 1971, Bush had recently lost a bid for election to the Senate, and was serving as President Richard Nixon's ambassador to the United Nations, a role he filled until 1973.
Bush was president of the USA from 1989-1993 and brought a "dedication to traditional American values" and a determination to make the US a "kinder and gentler nation", according to a White House biography.
At Bush clan gatherings, the two reputedly referred to each other as "Forty-one" and "Forty-three", referencing their respective numbers in the sequence of United States presidents.
George W Bush would go on to be elected president in 2000 after Mr Clinton and served two terms.
Other former commanders-in-chief also hailed the 41st president's legacy.
Bush is survived by his sons, former President George W. Bush, former Florida Gov. Jeb Bush, Neil Bush, Marvin Bush, and daughter Dorothy Bush Koch.
Bush died at 10.40pm CT on Friday, his office confirmed in a statement.
Former President George H.W. Bush listens to the national anthem with Airmen from the 380th Air Expeditionary Wing in 2006
Sitting alongside German Chancellor Angela Merkel, he refused to answer whether he had any regrets over his past criticism of the Bushes.
Trump tweeted against about Bush's death in the morning.
Former President George H.W. Bush has died at the age of 94.
Over 6,000 people attended Mrs Bush's funeral.
George Snr was the patriarch of one of America's most formidable political dynasties.
Trump mocked the "points of light" phrase at some of his campaign rallies this year. "Thousand points of light, I never quite got that one".
George H.W. Bush was an American hero and icon, he was a friend to all he met, he embodied class and dignity.
That partly explains why the Republican was willing to violate his "no new taxes" pledge with the budget agreement of 1990, which hurt him politically yet set the stage for a decade of increasingly sound federal budgets.
At a summit meeting in Malta in December 1989, Bush and Mikhail Gorbachev, his Soviet counterpart, declared an end to the Cold War and talked of a new era of "lasting peace".
The elder Bush's cautious realpolitik would later be contrasted to his son's far more costly ambition to transform the Middle East, but "Bush 41" refused to weigh in on the debate, insisting he was proud of the presidency of "Bush 43". "And through all that he accomplished, he remained humble, following the quiet call to service that gave him a clear sense of direction".More news: MS senator banking on boost from Trump rallies
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