The Internet Corporation for Assigned Names and Numbers (Icann) said the "fantastically complicated technical feature" allowing IDNs would represent the "biggest change" to the coding that underlies the internet since it was invented four decades ago.
BBC technology correspondent Mark Gregory says in the early days of the internet, language posed no problem, as most web-surfers spoke English and those that did not usually wrote in languages based on the Latin alphabet.
But this is no longer true, adds our correspondent.
Icann said it would accept the first applications for IDNs by 16 November, with the first up and running by "mid-2010".
It is likely the majority of early non-Latin net addresses to be approved will be in Chinese and Arabic script, followed by Russian.
Some countries, such as China and Thailand, have already introduced workarounds that allow computer users to enter web addresses in their own language.
However, these were not internationally approved and do not work on all computers.
Our correspondent says the point of the Icann vote was to create a universal internet address code that will work in any language and every place so all the world's computers can connect with each other.
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