DotAsia is an organisation consisting of groups that run domain names for countries such as Japan, China, Vietnam and South Korea.
The ".asia" domain will supplement individual countries' - ".jp" for Japan and ".cn" for China, for instance - bringing the total number of internet suffixes to 266.
ICANN earlier approved ".eu'" for the European Union.
DotAsia plans to explore permitting domain names in Asian scripts under ".asia".
ICANN also has been exploring allowing suffixes in other scripts, too.
Registration for names using the Latin alphabet is expected to open in six to nine months.
Trademark holders will get priority and prices will vary.
Plans are to restrict registration to those in the region, which includes Australia.
Demand for the new names has generally been low, compared to long-standing ones such as ".com", although some late-comers to the internet have found that the names they seek have been taken.