Leaders from within the Muslim world and from the wider international community were swift to criticise the move, and warned of the potential for violence and bloodshed as a result.
Mr Trump also approved moving the US embassy from Tel Aviv to Jerusalem, making America the first country in the world to officially recognise Jerusalem as Israel's capital.
The status of Jerusalem lies at the heart of the long-running Israeli-Palestinian conflict, as the Palestinians claim East Jerusalem as the capital of their future state.
White House officials have said Mr Trump's decision is a "recognition of current and historic reality" but is not a political statement, and will not change the physical and political borders of Jerusalem.
President Mahmoud Abbas said the decision was tantamount to the United States "abdicating its role as a peace mediator" after a decade of sponsoring the Israeli-Palestinian peace process.
"These deplorable and unacceptable measures deliberately undermine all peace efforts," he said in a speech after Mr Trump's announcement.
He insisted that Jerusalem was the "eternal capital of the state of Palestine".
Palestinian Islamist group Hamas chief Ismail Haniyeh said: "Our Palestinian people everywhere will not allow this conspiracy to pass, and their options are open in defending their land and their sacred places."
Israel's Prime Minister Benjamin Netanyahu said President Trump's announcement was a "historic landmark."
He called the US president's decision "courageous and just."
The Israeli prime minister said the speech was "an important step towards peace, for there is no peace that doesn't include Jerusalem as the capital of the State of Israel".
He said that the city had "been the capital of Israel for nearly 70 years".
Education Minister Naftali Bennett also hailed the decision, saying "the United States is adding another brick to the walls of Jerusalem, to the foundation of the Jewish nation", and urged other nations to follow Mr Trump's lead.
The Turkish Foreign Minister Mevlut Cavusoglu said the decision was "irresponsible."
He wrote on Twitter that "the decision is against international law and relevant UN resolutions".
Saudi Arabian media say King Salman told Mr Trump by telephone: "Any declaration on the status of Jerusalem before reaching a final settlement would harm the peace negotiation process and escalate tension in the region."
His views were echoed by President Abdul Fattah al-Sisi of Egypt, who warned against "complicating the situation in the region by introducing measures that would undermine chances for peace in the Middle East".
The Arab League called it "a dangerous measure that would have repercussions" across the region, and also questioned the future role of the US as a "trusted mediator" in peace talks.
The supreme leader of Iran, Ayatollah Ali Khamenei, said: "It is out of despair and debility that they want to declare Jerusalem as capital of the Zionist regime. On the issue of Palestine, their hands are tied and they can't achieve their goals."
Meanwhile, Jordan's King Abdullah called for joint efforts to "deal with the ramifications of this decision and to counter any action that undermines the Palestinian people's aspirations for their own independent state, with East Jerusalem as its capital".
Pope Francis said: "I cannot silence my deep concern over the situation that has emerged in recent days. At the same time, I appeal strongly for all to respect the city's status quo, in accordance with the relevant UN resolutions."
United Nations spokesman Stephane Dujarric told reporters: "We have always regarded Jerusalem as a final-status issue that must be resolved through direct negotiations between the two parties based on relevant Security Council resolutions."
The European Union called for the "resumption of a meaningful peace process towards a two-state solution" and said "a way must be found, through negotiations, to resolve the status of Jerusalem as the future capital of both states, so that the aspiration of both parties can be fulfilled".
French President Emmanuel Macron said Mr Trump's decision to recognise Jerusalem as Israel's capital was "regrettable".
He called efforts for "avoid violence at all costs."
Both China and Russia also expressed their concern that the move could lead to an escalation of tensions in the region.
UK Prime Minister Theresa May said she intended to speak to the President Trump about the issue.
"The status of Jerusalem should be determined in a negotiated settlement between the Israelis and the Palestinians," Mrs May said.
The city "should ultimately form a shared capital between the Israeli and Palestinian states", the prime minister added.