Trump's candidacy had been supported by few world leaders and his shock victory led to a collapse in global financial markets.
However, his victory over Hillary Clinton was welcomed by others.
Russian President Vladimir Putin, in a telegram to Trump, "expressed hope for mutual work on bringing US-Russia relations out of their critical condition".
Hungarian Prime Minister Viktor Orbán, who leads a right-wing coalition with a strong anti-immigration stance, commented, "Congratulations. What great news. Democracy is still alive."
British Eurosceptic MEP Nigel Farage, interim leader of Ukip and who played a key role in Britain's shock vote in June to leave the EU, tweeted:
"I hand over the mantle to @realDonaldTrump! Many congratulations. You have fought a brave campaign."
French MEP Marine Le Pen, head of the far-right anti-immigration National Front (FN) party, also praised Trump’s win, saying, "Congratulations to the new President of the United States Donald Trump and to the free American people".
In a tweet, Matteo Salvini, leader of Italy's far-right anti-immigration party the Northern League, declared, "Now it's our turn."
Elsewhere, the Palestinian President Mahmud Abbas, through a spokesperson, said, "We are ready to deal with the elected president on the basis of a two-state solution and to establish a Palestinian state on the 1967 borders."