The new stores opened as the firm, the world's biggest company by market value, seeks further growth in emerging markets, which saw a 63 percent increase in revenue for Apple in its last fiscal year.
Some customers queued for hours outside the new Dubai store on the second floor of the Mall of the Emirates, including Omani Mahmud Jawad, who drove more than 400 kilometres (250 miles) from Muscat with a friend to attend the opening.
"They will be successful here like they have been elsewhere in the world," he said.
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Apple products were previously available in the United Arab Emirates but not in one of Apple's own retail outlets.
The country, which is home to 10 million people including nine million foreigners, has become a regional commercial centre and tourist destination.
Last year, it welcomed 13.2 million tourists and is hoping to attract 20 million visitors in 2020, notably to its shopping hub of Dubai.
In Abu Dhabi, the Apple Store opened in Yas Island, near the Emirati capital's Formula 1 circuit.