A Wizz Air plane from Budapest was the first passenger aircraft to land at the sprawling new facility, and it was welcomed on the tarmac with a water cannon salute.
Jazeera Airways, another low-cost carrier, will follow suit on Thursday with daily flights to and from Kuwait, while Bahrain's national carrier, Gulf Air, will begin operations on December 8.
No other airlines have announced intentions to use the new airport, which lies some 50 kilometres (30 miles) south of Dubai International, one of the world's busiest hubs for air passengers.
Al-Maktoum International was opened only for cargo in June 2010, while passenger operations were repeatedly delayed.
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The new airport is situated in Dubai World Central, an economic zone the government hopes to turn into what it calls an "aerotropolis".
Once completed, it is to feature five runways that will be able to handle an annual capacity of 160 million passengers and 12 million tonnes of cargo.
It is part of a grand project announced during Dubai's economic boom, but the pace of progress slowed during the financial crisis that hit the Gulf emirate in 2009.