The status of Jerusalem is currently disputed between Israel and Palestine, with the city divided into East Jerusalem and West Jerusalem.
The Republican presidential candidate made the pledge at his Trump Tower home in New York during a meeting with the Israeli Prime Minister Benjamin Netanyahu.
A statement released by his campaign team said: "Mr Trump acknowledged that Jerusalem has been the eternal capital of the Jewish People for over 3000 years, and that the United States, under a Trump administration, will finally accept the long-standing Congressional mandate to recognize Jerusalem as the undivided capital of the State of Israel."
Tel Aviv, not Jerusalem (pictured), is largely recognised as the capital city of Israel.
Trump, who has known Netanyahu "for many years" also expressed support for US military assistance provided to Israel and he called upon Palestinians to "renounce hatred and violence and accept Israel as a Jewish State".
His campaign team added: "Mr Trump said that under a Trump administration, there will be extraordinary strategic, technological, military and intelligence cooperation between the two countries.
"Mr Trump recognized Israel as a vital partner of the United States in the global war against radical Islamic terrorism."
Meanwhile, the Democrat presidential candidate Hillary Clinton also met Israel's PM for an "in-depth conversation" and, according to her campaign, "reaffirmed unwavering commitment" to United States' relationship with Israel.
Foreign policy is expected to feature prominently during the first presidential debate held by Clinton and Trump on Monday night (local time).