The El Al airliner made the three-hour trip, carrying a delegation of Israeli and US officials.
The flight was allowed to cross Saudi Arabian airspace, normally blocked to Israeli air traffic.
The UAE has become only the third Arab country in the Middle East to recognise Israel since its founding in 1948.
On Saturday, the UAE repealed a law boycotting Israel which had been in place since 1972, and last month the two countries opened direct telephone services for the first time.
The agreement to normalise relations - brokered by the US - was made public in a surprise announcement on 13 August.
Flight LY971 - numbered to represent the UAE's international dialling code - carried delegates including Donald Trump's son-in-law and senior adviser Jared Kushner and Israel's National Security Adviser Meir Ben-Shabbat.
Kushner led secret talks which resulted in the agreement between Israel and the UAE, a federation of seven Arab monarchies in the Gulf, including Dubai.
Speaking to the media after landing in the UAE capital Abu Dhabi, Kushner described the deal between the countries as a "historic breakthrough" and said it was a "tremendous honour" to have joined the flight.
"What happened here was three great leaders came together and they started writing a new script for the Middle East. They said the future doesn't have to be predetermined by the past," he said
The joint teams will meet Emirati representatives to develop areas of co-operation between Israel and the UAE. The return flight will be numbered LY972, after Israel's international dialling code.
In a tweet in Hebrew, Israeli Prime Minister Benjamin Netanyahu hailed the advent of the flight as an example of "peace for peace" - alluding to his long-held disbelief in the notion that only trading occupied land will bring peace between Israel and Arab countries.
While it was welcomed by much of the international community, the UAE's recognition of Israel without the precondition of the creation of a Palestinian state was denounced by the Palestinians as a betrayal of their cause.
In return for official relations with the UAE, Netanyahu agreed to suspend controversial plans to annex parts of the occupied West Bank - land claimed by the Palestinians for a future state of their own.