French President Francois Hollande, who had earlier said Trump made him want to retch, expressed his reservations over his victory, saying "opens a period of uncertainty."
"This American election opens a period of uncertainty," he said in a statement that offered only brief congratulations to the controversial billionaire.
German Chancellor Angela Merkel said that any "close cooperation" between the US and her country must be based on shared democratic values, and reminded him of the global responsibility he carries.
"On the basis of these values, I offer close cooperation to the future president of the United States of America, Donald Trump," she said.
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US' close ally and British Prime Minister Theresa May lauded Trump's victory, saying the two countries had an "enduring and special relationship" and would remain "close partners" in trade, security and defence.
"I would like to congratulate Donald Trump on being elected the next US president following a hard-fought campaign. Britain and the United States have an enduring and special relationship based on values of freedom, democracy and enterprise," May said in a statement issued by Downing Street.
Putin "expressed hope for mutual work on bringing US- Russia relations out of their critical condition as well as on working out outstanding issues on the international agenda" in his congratulatory telegram, the Kremlin said.
China's President Xi Jinping sent congratulations to Trump and said he looked forward to working with him, state broadcaster CCTV reported.
"I highly value China-US relations, and look forward to working together with you, and holding fast to mutual respect and non-conflict, non-confrontation," the channel cited Xi as saying in its nightly national broadcast.
possibility" of its nuclear deal with world powers being overturned by Trump despite his threat to dismantle it.
"Iran's understanding in the nuclear deal was that the accord was not concluded with one country or government but was approved by a resolution of the UN Security Council and there is no possibility that it can be changed by a single government," state television quoted Rouhani as telling his cabinet.
Saudi King Salman, meanwhile, expressed hope that Trump would bring stability to the Middle East.
"We wish your excellency success in your mission to achieve security and stability in the Middle East and worldwide," Salman said.
Canadian Prime Minister Justin Trudeau pledged to work "very closely" with Trump, saying "Canada has no closer friend, partner, and ally than the United States".
"We look forward to working very closely with President-elect Trump, his administration, and with the United States Congress in the years ahead, including on issues such as trade, investment and international peace and security," Trudeau said in a statement.
"I congratulate Mr Trump and I wish him success," Prime Minister Binali Yildirim said in a speech in Ankara. He said that he has urged Trump to extradite as soon as possible the US-based Turkish preacher Fethullah Gulen, who Ankara accuses of masterminding the July coup bid.
Meanwhile, former Swedish Prime Minister Carl Bildt invoked Brexit on Twitter, saying, "looks like this will be the year of the double disaster of the West".
Sri Lankan President Maithripala Sirisena and Prime Minister Ranil Wickremesinghe also greeted Trump on his historic win, taking to the microblogging site to extend their wishes.
"Congratulations to President elect for this historic win. Your path to the White House has indeed been truly remarkable," Wickremesinghe said.