Though uncertainty remains over Trump's trade, immigration and geopolitical policies, investors appeared somewhat soothed by his victory speech, in which he praised Clinton and urged Americans to "come together as one united people" after a deeply divisive campaign.
In Europe, Germany's DAX was down 0.9 per cent at 10,384 while the FTSE 100 index of leading British shares was 0.2 per cent lower at 6,832.
US stocks are expected to open lower, too, though by far less than earlier predicted. Dow futures are 1.3 per cent lower at 18,057 while the broader S&P 500 futures were down 1.5 per cent at 2,103.
As Trump gained the lead in the electoral vote count, investors became increasingly uneasy and share prices tumbled in Asia, which were open during the election results. Dow futures were down 4 per cent at one point. However, by the time Trump was confirmed the winner and made his speech, financial markets had steadied.
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One currency that remains heavily sold is the Mexican peso. It was down 8.2 per cent at 45 US cents as the prospect of a wall along the United States' southern border, a key campaigning point for Trump, has come one step closer to reality. Trump has insisted that Mexico will pay for the wall.
"If Trump is able to follow through with these suggestions, Mexican activity will suffer greatly," said Jane Foley, senior foreign exchange strategist at Rabobank International.
Under the US constitution, Trump doesn't formally take the reins of power until January but he will begin the transition to his presidency almost immediately.