Sheikh Mohammed bin Rashid announced the achievement, saying Dubai had reached a "new phase in its journey towards a bright future".
The billionth passenger was nine-year-old Arjun who arrived at Dubai International with his family on Thursday afternoon, where they were told they will experience four days of the best Dubai has to offer.
"Dubai International Airport received its one billionth passenger today, marking a new phase in its journey towards a bright future," the Vice President and Ruler of Dubai said. "One billion passengers have made DXB a part of their personal story and helped shape Dubai into a global hub," he added.
Special Report: From sand runway to a billion passengers
Arjun and his older brother Varun, 13, were travelling with their mother Ramya and father Venkatesh on an Emirates flight from Orlando which arrived at 12:30pm.
Arjun and his family will stay at the Atlantis Hotel, ferried around by a Tesla limousine and experience four days of Dubai luxury including a guided tour of the Burj Khalifa, a personal shopping experience at Dubai Mall, backstage access and tickets to La Perle, a day at the Aquaventure water park and a private desert safari.
The family were selected at random from flight EK220, which was forecast to hold the billionth passenger.
They were greeted by Sheikh Ahmed bin Saeed Al Maktoum, President of the Dubai Civil Aviation Authority and CEO and Chairman of Emirates Group, who welcomed them to their first visit to Dubai.
"This landmark billionth passenger achievement is the result of teamwork and collaboration, and special thanks go out to each and every member of the airport community who have played a role in this journey," Sheikh Ahmed said.
He added, "of course, we would not be in this position if it were not for the visionary leadership of His Highness Sheikh Rashid bin Saeed Al Maktoum and His Highness Sheikh Mohammed bin Rashid Al Maktoum, Vice President, Prime Minister and Ruler of Dubai, both of whom foresaw the development of Dubai into a global centre for trade, tourism and commerce enabled by a fast-growing and world-leading aviation sector with top-flight airport infrastructure."
Pictures show Arjun clapping after hitting a red button on a podium, triggering a cascade of confetti from the ceiling.
Sheikh Mohammed said Dubai was "committed to remaining the first choice in transporting people across borders, helping them fulfil dreams, meet loved ones, and discover the world’s wonders".
The airport, which is the world's busiest by international passenger traffic, opened in 1960 with a 1,800-metre runway made of compacted sand.
It took 51 years to reach its 500 millionth passenger, who flew on December 31 2011, but only seven more years to welcome the next half-a-million.
This year, the airport expects to cater to more than 90 million passengers through three terminals. About 2.65 million tonnes of cargo travel through the airport each year.
The airport has grown considerably over the years, reflecting the development of the emirate. There are now three terminals and the world's first and largest purpose-built A380 facility.
Since 2015, it has been the world's third largest airport by passenger traffic, beaten only by Beijing Capital International Airport and Hartsfield-Jackson Atlanta International Airport.
The airport is the home base for Emirates Airlines and low-cost sister airline flydubai.
Dubai International Airport over the years:
It is also a hub of innovation in the commercial passenger industry, being the first airport to trial face-scanning tunnels which could replace immigration officers.
India, the UK and Saudi Arabia were the airport's top destinations in October, with nearly one million passengers travelling to India.
Next year, airlines at Dubai International Airport will reduce flights for 45 days while the southern runway is closed for resurfacing and replacement of ground lighting.