Until now, the ad-supported music streaming service was only available in the U.S., but as of Feb. 11, Australia can also tune in.
The service, announced at last June's Worldwide Developers Conference, offers users access to 100 radio stations, based on genre, artist or theme. It's free to listen to but is supported by advertising.
iTunes Radio went live in the U.S. in September and now it is moving further afield, starting with Australia.
As well as preprogrammed stations, the service offers exclusive first plays of upcoming albums from leading musicians and is an intelligent service in that it improves the more it is used.
Like a number of other streaming services, iTunes Radio learns about its users and their tastes from the songs they choose to listen to as well as the tracks already in their iTunes library.
The service can be accessed on any iOS7 supporting device -- an iPhone, iPad or iPod Touch, as well as the Apple TV set top box or via the iTunes application on desktop and laptop PCs.
Apple device owners who already pay to use the iTunes Match service that enables them to store and stream their music collections from Apple's iCloud can listen to iTunes Radio ad-free.
Two weeks ago, consumers in the U.K., Australia, Canada and New Zealand started reporting that they were getting intermittent access to iTunes Radio -- that its features were appearing and disappearing on their iOS devices, suggesting that Apple was gearing up to launch the service beyond the U.S.
Tuesday's official announcement proves that it's coming and that the next countries to get access are most likely to be the U.K. and Canada.
It took just one month for iTunes Radio to clock up 20 million users in the U.S., although data suggests that people are using it alongside other internet radio stations services, such as Pandora, rather than as a replacement.