Under the terms of the deal, Israel has agreed to suspend its controversial plans to annex parts of the occupied West Bank.
Israeli Foreign Minister Gabi Ashkenazi tweeted on Sunday that the two sides "decided together on the establishment of a direct communication channel ahead of the signing of the normalisation agreement between the two countries and ... to meet soon".
Israel's communications ministry said telecoms providers in the UAE had unblocked calls to numbers with Israel's +972 country code. "I congratulate the United Arab Emirates on the unblocking," said Israeli Communications Minister Yoaz Hendel.
"Many economic opportunities will now open up and these trust-building steps are important for advancing the countries' interests."
The two sides are expected to sign the accord in Washington in three weeks' time. Normalising relations will include opening embassies on each other's territory.
In another sign of the new, closer relationship, the two countries signed an agreement on Saturday relating to Covid-19 research.
Until now Israel has had no diplomatic relations with Gulf Arab countries. But shared concerns over Iran have led to unofficial contacts between them.
The agreement reportedly took Palestinian leaders by surprise. A spokesman for President Mahmoud Abbas said the deal amounted to "treason".
Since Israel's declaration of independence in 1948, it has only signed peace deals with two other Arab countries - Egypt in 1979 and Jordan in 1994. Mauritania, a member of the Arab League in north-west Africa, established diplomatic relations with Israel in 1999 but severed ties in 2010.
Trump has said he expects more Arab and Muslim countries to sign treaties with Israel.
Israeli Prime Minister Benjamin Netanyahu said he had "delayed" West Bank annexation plans, but those plans remained "on the table". Annexation would make some West Bank areas officially part of Israel, dealing a blow for Palestinian plans for a state of their own.
Trump's chief adviser, Jared Kushner, said that told he and President Trump had been working on a deal between Israel and the UAE since Trump came to office.