Apple's senior vice president of Internet Software and Services Eddy Cue (L) high fives with recording artist Drake during the Apple Music introduction at the Apple WWDC on June 8, 2015 in San Francisco, California / Getty Images

None of those users are paying, yet — though Apple will automatically move them over to start paying

Apple has signed up 11 million new users to its streaming music service since it launched at the end of June.

"We're thrilled with the numbers so far," Eddy Cue, who runs Apple Music alongside other Apple internet services, told USA Today.

Apple Music went live on June 30, cost £9.99 per month in the UK or £14.99 for the family plan. But for the first three months, users won’t pay anything.

Customers will be automatically switched over to the paid-for service at the end of that trial period, in October, unless they have told Apple in advance that they don’t want to opt in for auto-renewals. (Opting out of those auto-renewals is simple but not obvious.)

If all of the current members do stay on, then Apple will have half as many paying customers as Spotify, its closest rival. But Spotify has many more members on its free tier — an option that Apple Music won’t offer.

The Apple Music family plan allows six different people to use one subscription, for £14.99. Of the 11 million already signed up, 2 million have chosen that option, Cue said.

Some new adopters of the service have run into problems with the sign up process, which can sometimes duplicate or disappear music. Cue told USA Today that Apple is "aware that some users have experienced some issues, and we hate letting them down, but we're releasing updates as fast as we can to address those issues."

Apple does have the advantage that its streaming service comes bundled with the Music app on iPhone and iPad, and iTunes on Macs. That means that when a user opens the app for the first time since upgrading, they’ll see a message and invitation to set themselves up with Apple Music.

But the 11 million users must all be on Apple’s computers or mobile devices, or PCs — not on Android. The company isn’t launching its Android app for Music until the autumn, and so Spotify has a broader potential base of customers since it is available for all of the major platforms.