The head of state was welcomed to Abu Dhabi's presidential terminal by Sheikh Abdullah bin Zayed, Minister of Foreign Affairs and International Co-operation.
Mr Herzog was accompanied by his wife, Michal, known as Israel's first lady, for the two-day visit.
At Qasr Al Watan, the presidential palace, artillery fired 21 rounds as Mr Herzog was greeted by Sheikh Mohamed bin Zayed, Crown Prince of Abu Dhabi and Deputy Supreme Commander of the Armed Forces. The national anthem of both nations was played as guards saluted the Israeli president, state news agency Wam said.
In a tweet, Sheikh Mohamed bin Zayed said: "Today in Abu Dhabi I met with President of Israel Isaac Herzog. We discussed our bilateral relations, regional issues of mutual interest, and the importance of exploring further opportunities to build bridges of cooperation and friendship between our two nations."
On Twitter, Mr Herzog posted a message in Arabic thanking the Emirates for the warm reception.
In a later statement from his government, the president said: “We are sending a message to the entire region that there is an alternative of peace and living together, and that the sons and daughters of Abraham can reside and dwell together in peaceful coexistence for the benefit of humanity.
“The citizens of the State of Israel are so moved and excited to continue and develop the peaceful coexistence and our peace agreement between our two nations, the Emiratis and Israelis.
“I am very much looking forward to my visit at the Expo and seeing the most unbelievable experience that everyone is talking about, including the 250,000 Israelis who have already set foot in your beautiful country."
Wam said: "His Highness welcomed [Mr] Herzog and expressed his hope that this visit would contribute to advancing the relations between the two countries to a higher level for the higher good of their peoples and those of the region.
"The two sides also reviewed the prospects of growing cooperation at all levels, especially in the economic, trade, investment, development, technology, health, and other fields."
Dr Anwar Gargash, diplomatic adviser to President Sheikh Khalifa, shared a message online describing the visit as fitting in with the UAE's pursuit of improving relations with all its neighbours.
"The historic visit of Israeli President Isaac Herzog to the UAE comes within the framework of Israel's participation in the Dubai Expo, with the aim of developing bilateral relations inaugurated by the Abraham Accords and within the UAE's endeavour to build and strengthen bridges with all countries in the region and towards developing regional prosperity and stability," he wrote.
On Twitter, US Secretary of State Antony Blinken said the US “warmly welcomed this historic visit and the deepening of ties between our friends in the region”.
Michal Herzog held a meeting with Sarah Al Amiri, Minister of State for Advanced Technology.
On Monday, Mr and Mrs Herzog will attend Israel's day of celebrations at Expo 2020 Dubai.
Mr Herzog, who took up the post last year, is the son of Chaim Herzog, who served as president of Israel from 1983 to 1993.
Last week, he said: “We have the privilege of making history by making the first visit of an Israeli president to the United Arab Emirates.
“I thank Sheikh Mohamed bin Zayed for this gracious invitation to deepen our nations' bonds of friendship.”
In December, Prime Minister Naftali Bennett became Israel's first leader to visit the Emirates following the normalisation of ties between the two countries in 2020, meeting Sheikh Mohamed and other senior leaders.
Since the UAE formally established ties with Israel, through the signing of the Abraham Accords in September 2020, much work has been done to bolster the friendship. Last year, the UAE Cabinet approved the opening of an embassy in Tel Aviv.
Israel opened an embassy in Abu Dhabi with the arrival of a temporary envoy, Eitan Na'eh, who was later succeeded by the first permanent ambassador, Amir Hayek.
Israel has a substantial presence at Expo 2020 Dubai with a large pavilion, frequent visits from dignitaries and television crews, and a host of events over the past four months.
Ministers and senior government figures who attended the presidential palace event included: Sheikh Mansour bin Zayed, Deputy Prime Minister and Minister of Presidential Affairs, Sheikh Abdullah bin Zayed, Minister of Foreign Affairs and International Co-operation, Sheikh Hamdan bin Mohamed bin Zayed, Dr Sultan Al Jaber, Minister of Industry and Advanced Technology and Khaldoon Al Mubarak, chairman of the Executive Affairs Authority.