He was received by Abu Dhabi's Crown Prince Sheikh Mohamed bin Zayed Al Nahyan and accorded a ceremonial welcome at the airport.
Modi is here on a two-day official visit that will see talks focused on boosting cooperation in energy and trade.
In a significant gesture, five brothers of the crown prince were also present at the Abu Dhabi Presidential Airport to receive Modi, according to tweets by external affairs ministry spokesperson Vikas Swarup.
"For Crown Prince and his five brothers to receive a dignitary is a rare gesture reflecting imp attached to PM's visit," tweeted Swarup.
Modi is the first Indian prime minister to visit the UAE after the 1981 visit of then prime minister Indira Gandhi.
Ahead of his visit, Modi said in an interview to Khaleej Times: "We have a range of common security and strategic concerns in the region, including terrorism and extremism.
"So India and the UAE have everything to be a top priority for each other. This is the way I look at the UAE. The Gulf region is vital for India's economic, energy and security interests."
"I want to see the UAE as our foremost trade and investment partner. We would build regular and effective cooperation in a full range of security challenges. Our armed forces would engage with each other more.
"We will work together more closely in international forums and in addressing regional challenges. There are no limits to our relationship," Modi said.
Modi also described the UAE as a "Mini India" and vowed to build a "regular and effective cooperation in security challenges".
The UAE is home to 2.6 million Indian expatriates.
"I have begun my regional engagement with the UAE. This tells you the importance I attach to the UAE. We have resolved to sustain regular high level engagements and build a strong and comprehensive strategic partnership."
Modi will hold official talks with the leadership of Abu Dhabi and later visit Masdar City, a planned city project in Abu Dhabi, where he is expected to spend some time watching presentations.
Later, he will meet business people and focus on investments.
On Monday, he will first visit the Sheikh Zayed Grand Mosque in Abu Dhabi and later travel to Dubai, where after meeting the Dubai ruler, he will attend a grand public reception hosted for him at the Dubai Cricket Grounds.
The public reception, which begins at 7.30 p.m., is expected to see 50,000 Indian expatriates attending.