The announcement makes the UAE the first Gulf Arab state to do so and only the third Arab nation to have active diplomatic ties to Israel.
Mr Trump tweeted a statement from the countries acknowledging the deal.
He then told reporters in the Oval Office it was “a truly historic moment.”
“Now that the ice has been broken I expect more Arab and Muslim countries will follow the United Arab Emirates,” he said.
The recognition grants a diplomatic win to Mr Trump ahead of the November election.
His efforts to see an end to the war in Afghanistan have yet to come to fruition, while efforts to bring peace between Israel and the Palestinians have made no headway.
For Israel, the announcement comes after years of boasting by Israeli Prime Minister Benjamin Netanyahu that his government enjoys closer ties to Arab nations than publicly acknowledged.
Mr Netanyahu has sought to build settlements on lands sought by the Palestinians and embraced a US proposal that would allow him to annex large parts of the occupied West Bank while granting Palestinians limited autonomy in other areas.
For the UAE, it further enhances its international campaign to be seen as a beacon of tolerance in the Middle East despite being governed by autocratic rulers.
It also puts the UAE out first in a regional recognition race among neighbouring Gulf Arab states.
Israel got rewarded for not declaring openly what it's been doing to Palestine illegally & persistently since the beginning of the occupation. The UAE has come out in the open on its secret dealings/normalization with Israel. Please don't do us a favor. We are nobody's fig leaf! https://t.co/6e8x7EhF2v
Advertisement— Hanan Ashrawi (@DrHananAshrawi) August 13, 2020
For the Palestinians, who long have relied on Arab backing in their struggle for independence, the announcement marked both a win and setback.
While Thursday’s deal halts Israeli annexation plans, the Palestinians have repeatedly urged Arab governments not to normalise relations with Israel until a peace agreement establishing an independent Palestinian state is reached.
Senior Palestinian official Hanan Ashrawi said on Twitter that the deal perpetuates Israel’s occupation of the West Bank.
She wrote: “Israel got rewarded for not declaring openly what it’s been doing to Palestine illegally & persistently since the beginning of the occupation.”
Ms Ashrawi also said the UAE has come forward with its “secret dealings/normalization with Israel”.
The militant group Hamas, which controls the Gaza Strip, called the deal by the Emiratis “a stabbing in the back of our people”.
Blessed are the peacemakers. Mabruk and Mazal Tov
A joint statement from the US, the UAE and Israel was issued immediately after Mr Trump’s tweet.
It said delegations will meet in the coming weeks to sign deals on direct flights, security, telecommunications, energy, tourism and healthcare.
The two countries also will partner on fighting the coronavirus pandemic.
“Opening direct ties between two of the Middle East’s most dynamic societies and advanced economics will transform the region by spurring economic growth, enhancing technological innovation and forging closer people-to-people relations,” the statement by Mr Trump, Mr Netanyahu and Abu Dhabi Crown Prince Mohammed bin Zayed Al Nahyan, the day-to-day ruler of the UAE, said.
US Secretary of State Mike Pompeo praised the deal.
“This is a remarkable achievement for two of the world’s most forward leaning, technologically advanced states, and reflects their shared regional vision of an economically integrated region,” he said in a statement.
“It also illustrates their commitment to confronting common threats, as small – but strong – nations.”
He added: “Blessed are the peacemakers. Mabruk and Mazal Tov.”
Among Arab nations, only Egypt and Jordan have active diplomatic ties with Israel.
Egypt made a peace deal with Israel in 1979, followed by Jordan in 1994.
Mauritania recognised Israel in 1999 but later ended relations in 2009 over the Israel’s war in Gaza at the time.