The company is no longer taking orders and will cease selling tracks and restrict access to current users only on 28 September. The site will close to all customers on 19 October.
"If you have purchased tracks from the service we recommend that you back up your music files," said Virgin Digital in a statement.
"If you are a current Club member you will be able to continue using the service until the date that your next payment is due, after which the service will no longer be accessible to you.
"To all our customers we would like to say thank you and offer our apologies for any inconvenience this might cause."
Users who bought their music can burn the files onto a CD and transfer them to a music player separately.
However, those who opted for a subscription model, where a monthly fee gives access to the whole catalogue, will lose all rights to the music in one month's time.
The closure is good news for Apple since it highlights the biggest flaw in subscription models for buying music. Apple has consistently stated that people want to buy, rather than rent, music.
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