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He becomes the first sitting vice president since 1836 to succeed to the Oval Office.
Mr Bush achieved a comfortable victory over Democrat Michael Dukakis, taking almost 54% of the popular vote, compared with 46% for his rival.
His electoral promise, "Read my lips, no new taxes", appears to have won more favour with the voters than Mr Dukakis's claim that the American economy was in trouble.
Early results yesterday showed strong support for Mr Bush. He had notched up victories in seven states before Mr Dukakis took his first.
But the 55-year-old Democrat nominee did fight back. His economic policies, with the slogan "I'm on your side" won support from key groups like the poor, the elderly, inner city dwellers and black voters.
Mr Bush garnered most of his support from the younger, better educated and better-off, as well as the vast majority of white voters.
The campaign between the two men has been described as one of the dirtiest of recent times.
The big issues like America's huge debts, its future international role and relations with the Soviet Union have been obscured by acrimonious exchanges on crime and personalities.
Mr Bush was accused of being a wimp for hiding behind Ronald Reagan during his eight years in power and there were also hints he had had an extra-marital affair.
For Mr Dukakis there was a suggestion he had undergone psychiatric treatment and that his wife, Kitty, had once burned the Stars and Stripes during a peace demonstration.
Mr Bush's running mate, Senator Dan Quayle of Indiana, also attracted a lot of mudslinging, with questions over his competency to become vice president.
Both contenders continued campaigning right up to the end with last-minute television appeals. In a paid 30 minute broadcast, Ronald Reagan gave a warm tribute to his loyal vice president.
He said: "George Bush is one of the ablest, one of the strongest men I've known in my life-time. I trust George Bush and America can trust him too."
Mr Dukakis referred, in his broadcast, to criticisms about his lack of warmth with this appeal: "I want you to know Michael Dukakis is someone who cares very, very deeply about his family, about his neighbours, about his fellow citizens and that is why I am running for president."
President George Bush took over the White House with 426 electoral college votes, compared with Michael Dukakis's 111.
He arrived at a time of great change in the world with the imminent collapse of the Eastern Bloc and the end of the Cold War. The Soviet Union also ceased to exist and Mikhail Gorbachev, whom the US had supported, resigned.
During his period in office, President Bush sent US troops into Panama where the corrupt regime of General Manuel Noriega was threatening the security of the canal and Americans living there.
But his greatest test was the Iraqi invasion of Kuwait in 1990. He rallied the UN and the Western World to attack Saddam Hussein's forces and Operation Desert Storm saw the Iraqi army routed and Kuwait freed, although Saddam Hussein remained in charge in Baghdad.
Despite President Bush's apparent successes overseas, he was unable to stem the rising tide of discontent at home over the economy and increasing crime. He had to break his election promise and raise taxes to try to reduce the growing federal deficit.
He lost his bid for re-election to Democrat Bill Clinton.
Then in November 2000, his eldest son George W Bush was elected president.
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