But the officials said Mr Trump would not immediately move the US embassy from Tel Aviv to Jerusalem.
The news comes ahead of an expected speech by Mr Trump on Wednesday.
Arab leaders earlier warned against moving the US embassy in Israel to Jerusalem, with one saying this would be “a flagrant provocation to Muslims”.
The status of Jerusalem – a holy site for Israelis and Palestinians – is extremely contentious.
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.
The issue goes to the heart of Israel’s conflict with the Palestinians, who are backed by the rest of the Arab and wider Islamic world.
The city is home to key religious sites sacred to Judaism, Islam and Christianity, especially in East Jerusalem.
Israel occupied the sector, previously occupied by Jordan, in the 1967 Middle East war and regards the entire city as its indivisible capital.
The Palestinians claim East Jerusalem as the capital of a future state, and according to 1993 Israel-Palestinian peace accords, its final status is meant to be discussed in the latter stages of peace talks.
Israeli sovereignty over Jerusalem has never been recognised internationally, and all countries maintain their embassies in Tel Aviv.
Since 1967, Israel has built a dozen settlements, home to about 200,000 Jews, in East Jerusalem. These are considered illegal under international law, though Israel disputes this.
In recognising Jerusalem as Israel’s capital, the US could reinforce Israel’s position that settlements in the east are valid Israeli communities.
The Trump administration officials said recognising Jerusalem as Israel’s capital was seen “a recognition of reality” by the US government.
However, specific boundaries of the city would remain subject to a final status agreement, the official said. The status of holy sites will not be affected.
Mr Trump also would direct the state department to begin the process of moving the US embassy to Jerusalem – but this could take several years.
He promised the move to pro-Israel voters during his campaign for the presidency.
The US officials added that the president would be signing a regular waiver blocking the embassy’s move from Tel Aviv to Jerusalem until the new building was completed.
Ahead of his formal announcement, Mr Trump phoned several regional leaders to tell them he intended to move the US embassy from Tel Aviv to Jerusalem.
Saudi Arabia’s King Salman bin Abdulaziz al-Saud told Mr Trump that the relocation of the embassy or recognition of Jerusalem as Israel’s capital “would constitute a flagrant provocation of Muslims, all over the world”.
The White House said the president spoke to Middle East leaders including Israeli Prime Minister Benjamin Netanyahu on Tuesday. (Courtesy BBC)