He is due to announce the controversial decision in a speech later, the BBC reports.
Mr Trump is also expected to approve moving the US embassy from Tel Aviv to Jerusalem, but not for several years.
Israel welcomes the changes but the Palestinians and Arab leaders have warned they will jeopardise any Middle East peace process.
Saudi Arabia, an ally of the US, called the changes “a flagrant provocation to Muslims”.
Israel has always regarded Jerusalem as its capital city, while the Palestinians claim East Jerusalem as the capital of a future Palestinian state.
In recognising Jerusalem as Israel’s capital, the US becomes the first country to do so since the foundation of the state in 1948.
