Prime Minister Benjamin Netanyahu expressed confidence that he and Trump can work together to bring US-Israeli relations to "new heights".
In a statement congratulating the Republican candidate, Netanyahu said: "President-elect Trump is a true friend of the State of Israel, and I look forward to working with him to advance security, stability and peace in our region."
"I am confident that President-elect Trump and I will continue to strengthen the unique alliance between our two countries and bring it to ever greater heights," said Netanyahu, who has had a rocky relationship with outgoing Democratic President Barack Obama.
President Reuven Rivlin also welcomed Trump’s victory. “I would like to congratulates the president-elect, Donald Trump, his family, and the American people as a whole, who have once again proven to the entire world the meaning of being the greatest democracy in the world.”
Warning the president-elect that many domestic and global “challenges stand at your doorstep,” Rivlin assured him that "Israel, the United States' strongest ally, stands by our friend and partner in any challenge that may come our way, and I have no doubt that the connections between the countries will continue and strengthen during Trump's presidency as well."
Jerusalem Mayor Nir Barkat also praised praised Trump as a “devoted supporter of Jerusalem,” adding that he expected the new administration to move the US embassy to the capital.
“I am full of hope for your support for our activities for building in and developing Jerusalem for all her residents, and I invite you to visit the capital of Israel,” Barkat wrote.
On a number of occasions, Trump has proposed moving the US Embassy to Jerusalem, even though the US has not recognized Israel's sovereignty over the eastern half of the city.
Russian President Vladimir Putin, to whom Trump repeatedly made overtures of cooperation during his campaign, was among the first to send a telegram expressing his hope that the two countries would move closer together despite the current Syrian conflict which has wrenched them ever further apart.
In a brief statement Wednesday, the Kremlin said Putin expressed "his hope to work together for removing Russian-American relations from their crisis state."
Putin also said he has "confidence that building a constructive dialogue between Moscow and Washington that is based on principles of equality, mutual respect and a real accounting for each other's positions, is in the interests of our peoples and the world community."
Egyptian President Abdel Fattah al-Sisi also sent his congratulations to Trump, saying that he hoped that his inauguration would bring with it “a new climate in the relations between Egypt and the United States and lead to greater cooperation and coordination in accordance with the interests of the Egyptian and the American nation.”
The Egyptian president also said he hoped a Trump administration would “strengthen peace, stability and development in the Middle East especially in light of the challenges which remain in the region”
British Prime Minister Theresa May congratulated Trump on his “hard-fought campaign” saying that she wanted the “special relationship” between the two countries to endure and that Britain and the United States would remain "strong and close partners on trade, security and defence".
The statement was more conciliatory than those previously made by May who before being appointed prime minister, criticised Trump's call for a ban on Muslims from entering the United States, saying it was divisive, unhelpful and wrong.
She also called his suggestion that parts of London were so radicalised that the police dare not enter them "nonsense", saying: "I think it shows that he doesn't understand the United Kingdom and what happens in the United Kingdom."
Palestinian President Mahmoud Abbas said in a statement that he "congratulates the elected American president, Donald Trump, and hopes that peace will be achieved during his term."
An Abbas aide, Saeb Erekat, added that he doesn't expect US positions on the Israeli-Palestinian conflict to change under Trump.
Erekat added that the Republican and Democratic parties are both committed to a two-state solution of the conflict and "I think this will not change with the coming administration."
Statements from Iran implored Trump to remain committed to the international nuclear deal with Iran, Iranian foreign minister Mohammad Javad Zarif was quoted as saying by Tasnim news agency on Wednesday.
Throughout his campaign, Trump consistently attacked the deal signed by President Obama and essentially pledged to cast it aside.
"The United States should fulfil its commitments in the Joint Comprehensive Plan of Action (the nuclear deal) as a multilateral international agreement," Zarif was quoted as saying while on a visit to Romania.
A host of other nations such as Turkey and Canada wished Trump congratulations but tensions between Mexico and the Trump camp, which had been heightened as a result of persistent invective during the latter’s campaign, were calmed by Mexican President Enrique Pena Nieto who said that the US and his country were friends and that they should continue to work together.
The warm wishes were not only forthcoming abroad. Democratic President Barack Obama called Trump and invited him to the White House on Thursday to discuss the transition of power, the White House said.
"Ensuring a smooth transition of power is one of the top priorities the president identified at the beginning of the year and a meeting with the president-elect is the next step," the White House press secretary said in a statement.
According to Trump’s campaign manager Kellyanne Conway the two had “a very warm conversation.” She told NBC’s “Today” program that "He was congratulated, and I think they resolved to work together."
Obama, who also called unsuccessful Democratic candidate Hillary Clinton, will make a statement on Wednesday to discuss the election results.
Conway also said Clinton's top aide, Huma Abedin, called her late Wednesday and connected Clinton with Trump. She said Clinton "congratulated him for his victory," and he told Clinton that she is "very smart, very tough" and had "waged a tremendous campaign."
Andrew Friedman/TPS also contributed to this article