The announcement was made at the AFC Congress in the Bahraini capital of Manama.
Saudi Arabia was the sole bidder after India withdrew in December.
"We are excited to deliver the greatest tournament in the competition's history," the kingdom's sports minister Prince Abdulaziz bin Turki Al-Faisal said after the announcement.
"The kingdom is transforming before our eyes and we are filled with excitement for what it will look like in 2027."
In the coming years the Saudis, who watched as neighbours Qatar hosted the World Cup in November and December, will hold the women's Asian Cup, the Olympic-sized Asian Games and even the Asian Winter Games on artificial snow.
Saudi Arabia is also eyeing a World Cup and Summer Olympics, perhaps even a Winter Olympics, together with a swathe of other major events.
"I'm sure Saudi Arabia will host a fantastic Asian Cup," FIFA President Gianni Infantino said at the Manama congress.
The 2023 Asian Cup will be hosted by Qatar. It was previously set to be held in China but the country withdrew because of Covid.
The Asian Cup is staged every four years. Qatar won the tournament's last edition, in 2019, which was hosted by the United Arab Emirates.
Saudi Arabia has won three AFC Asian Cup titles.