Two different editions of the magazine's first issue have been produced - one in English and one in Arabic.
Different images of Hadid in a sequined headscarf feature on the two covers.
Such a gorgeous image, though I wish they'd have used an Arabian model - those girls are so beautiful," wrote one follower of the Vogue Arabia account.
Another said: "Been waiting for this for so long 😍😍 maybe you'll give a chance to Arab models like what Harper's Bazaar did."
Vogue Arabia is the 22nd edition of the fashion publication to be launched.
It will be distributed in several Middle Eastern countries, including Qatar, Saudi Arabia, Bahrain, Kuwait, Oman and the United Arab Emirates.
A bilingual Arabic-English website for Vogue Arabia has already gone live, with the publication of the paper magazine to follow.
"The collage of countries across the Arab world are long-deserving of a place in fashion history," Abdulaziz said in her message published on the website.
"And there's no better first 'face' to lead the charge for Vogue Arabia than Gigi, a model who defines tomorrow's entrepreneurial and dynamic generation."
Hadid has mixed heritage - her mother is a Dutch-born American while her father is Palestinian-American.