Apple has rolled out its iTunes Match cloud music service to the UK and other parts of the world.
For a fee Apple scans users' libraries, allowing songs to be replaced with higher quality versions. These can then be accessed from other Apple devices.
The service has been described as an "amnesty for music pirates" although it does not formally protect users against copyright infringement prosecutions.
A glitch marred the launch, locking some users out of their accounts.
For a £21.99 annual charge, users can match and replace up to 25,000 songs stored on their computer, including CD-rips as well as tracks obtained by other means.
Apple said it does not change anything in users' music libraries unless they choose to download the firm's "high-quality" versions to replace their existing files.
If the initial scan finds songs it does not recognise on the user's hard drive, they are uploaded to Apple's servers.
Users can then download or stream the songs to other computers logged into their iTunes account, as well as to iPhones, iPads and other iOS devices. It removes a previous restriction that caused users to be charged if they downloaded songs for a second time from Apple's online store.
Music industry insiders have welcomed the launch.
"We believe that it creates a great and seamless experience for music buyers that will ultimately see increased sales and digital conversion," Paul Smernicki, director of digital for Universal Music UK, told the BBC.
Analysts had originally thought it would take Apple longer to get permission from record labels for the UK launch.
"The reason why this can happen is because Apple essentially owns the music industry's most valuable customers - the ones spending the lion's share in the digital marketplace," said Mark Mulligan, an independent digital analyst.
"The major record labels are more willing to do things in Apple's ecosystem than they would elsewhere."
Although Amazon and Google offer rival cloud music services, they have yet to offer them to UK customers.
Spotify allows users to stream music they do not own from its servers, but either imposes a 10 hours per month limit or charges a minimum £4.99 per month fee.
Experts say Apple is not focused on making its service a moneyspinner.
"It's not really a revenue generator for Apple, but is another way to make their devices more appealing and more painful to switch to a rival's device when it is time to upgrade," said Benedict Evans from Enders Analysis.
When the service launched in the US a month ago, reports noted that Apple had agreed to share the subscription fee with record labels - effectively helping them monetise illegal downloads.
"The record labels know that they will get more revenue from the matched content in iTunes than they do from their anti-piracy and lobbying efforts," said Mr Mulligan.
"This is also formal recognition that the majority of digital music consumers tend to get music from lots of sources, including illegal ones, as well as buying legitimate MP3s. The music labels may not say it but they now accept they will never win the war against piracy."
Mr Evans added that claims of an "amnesty" might have been overplayed.
"There is an argument that this launders your pirated music. But frankly as a consumer what difference does that make?" he said.
"The word amnesty implies there was some sort of penalty out there - frankly no-one was going to break down your door and tell you off. So this really doesn't change anything in practical terms."
The international launch of the service coincided with an apparent outage.
A search of Twitter revealed that subscribers across the world had complained that iTunes had refused to recognise their Apple IDs, and said access to Apple's other cloud services was also affected.
However, reports suggested that the problem had been fixed later in the day.
Apple told the BBC that the sign in process "is now working fine".