The three new stores will offer single downloads for a price of €0.99, or £0.79 in the UK, and a catalogue of over 700,000 songs for PC or Mac users to choose from.
According to Apple, users will be able to play songs on up to five personal computers, burn a single song onto CDs an unlimited number of times, burn the same playlist up to seven times and listen to their music on an unlimited number of iPods.
The US iTunes store launched at the end of April last year and quickly became the most successful fee-based service to date for authorised music downloads. The company sold one million downloads in its first week, and to date has sold more than 85 million songs.
Apple expects an EU-wide version of the store to open in October.
Peter Jamieson, chairman of the British Phonographic Industry, welcomed the announcement: "It's great news for the UK music industry, but it's even better news for UK music fans. Music fans now have the chance to sample, share, download and burn without breaking the law and taking the risks presented by illegal peer-to-peer file sharing."
But Apple's launch was marred by news that it has been unable to sign some independent labels, which account for up to 25% of all record sales in the UK.
The Association of Independent Music (AIM) yesterday announced that it had called a halt to negotiations with Apple, with the result that artists such as Franz Ferdinand, Craig David and So Solid Crew will not be available via iTunes, according to reports.
"We welcome the arrival of iTunes in the UK, but are disappointed that our members have been unable to agree terms for licensing their repertoire to the service," AIM's chief executive Alison Wenham told BBC Online.
Simon Wheeler, spokesman for the Beggars Group – which acts for labels with bands such as White Stripes and the Pixies on their books – told BBC Online: "It is the general terms. They came in very late in the day. We are being dictated what the terms will be for the next three years of a very young business."
Napster launched its equivalent service in the UK last month.