The relaxation in liquor laws is in part to prepare for visitors from Israel after a landmark deal to normalize relations.
Both the emirates are among seven in the United Arab Emirates federation.
"We are announcing the cancellation of permits for alcohol, and residents and tourists will have the right to buy it in authorised stores," said the circular from the Department of Culture and Tourism dated September 15 and seen by AFP on Tuesday.
The directive said buyers must be at least 21 years of age, that the alcohol must not be re-sold, and that it should be consumed in a private home or an authorised place such as a club.
But it did not specify whether Muslims are forbidden to buy alcohol or not. Formerly Muslims were not permitted to acquire an alcohol licence.
The circular ends a legal grey area in the emirate. Although liquor stores in Abu Dhabi do not usually ask for permits to sell alcohol, sales were technically still subject to those rules.
In Dubai, stores are required to ask residents or tourists to show a permit before selling alcohol, but bars and restaurants do not require patrons to produce the document.
This year, Dubai also relaxed the permit system, making it easier for residents to acquire one by removing the requirement to obtain a "certificate of no objection" from their employer.
Residents need only to fill out a basic form, present their identity card, and pay 270 dirhams ($74) to obtain the permit. Tourists can get a temporary licence by showing their passport and visas at the store.
However, Muslims still cannot apply for an alcohol permit in Dubai.
The sale of alcohol is permitted in six of the seven emirates in the UAE, but is prohibited in conservative Sharjah which remains "dry" with no pubs or bars. Public intoxication and drink-driving are strictly banned across the country.
(Writer & Editor: MH/SLS/DV, Agence France-Presse)
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