Mr Trump made the remarks in an interview with Israeli newspaper Israel Hayom, published on Friday. The holy city is contested by Israel and the Palestinians, who both claim it as their capital.
The inflammatory promise – made on the campaign trail – has been condemned by the international community.
Observers worry such a symbolic move could spark renewed violence in Israel and the Muslim world, and risks showing the US is no longer interested in pursuing a two-state solution.
Since taking office Mr Trump’s administration had approached his campaign rhetoric with more caution.
Despite enthusiasm from several prominent Israeli politicians, White House Press Secretary Sean Spicer told reporters last month that the US was only “at the very beginning stages of even discussing this subject.”
While the election of Mr Trump – who is regarded as far more sympathetic to Israeli interests than his predecessor Barack Obama – was welcomed in Israel, the president also used the Israel Hayom interview to say he does not think Israeli settlement building in the West Bank is “good for peace.”
The remarks represent the most direct comments Mr Trump has made on the subject since taking office.
Israel, emboldened by what one politician described as a “friend in the White House”, has pushed through plans for thousands of settler homes over the 1967 Green Line in the past few weeks. Last week the Knesset also voted to legalise around 4,000 homes already built on privately owned Palestinian land.
Palestinian officials have been outraged by both the new building plans and the proposed embassy move, which Palestinian Authority President Mahmoud Abbas wrote to Mr Trump to warn it could “open the gates of hell”. One senior Fatah member called the move “as good as as declaration of war.”
Jerusalem has already seen an upswing in stabbings and shooting attacks in the last 18 months in what has been dubbed the ‘Jerusalem intifada’.
Israeli media has reported that Prime Minister Benjamin Netanyahu’s cabinet has met for special consultations with police, security services and the Israel Defence Force (IDF) in preparedness for “scenarios of worsening violence” if the US does move its embassy to the city.
Army officials warned they expected violence could also spread to the West Bank.
Over the years several US presidential candidates have made the same pledge in an effort to reach out to Jewish American voters and assure Israel that strong relations with the country are a high priority for their administration, but none have followed through with the plan once reaching office.