Virgin said it would also offer an "entry level" service to fans that do not want unlimited access.
Those signing up will be able to put the tracks on any music player and keep the music they have downloaded even if they stop paying the monthly fee.
Artists such as Amy Winehouse, Girls Aloud, La Roux and Black Eyed Peas are signed to Universal.
Virgin said it had vowed to try a range of anti-piracy measures as part of the deal. The last resort would be a temporary suspension of a customer's internet connection if that person consistently ignored warnings about their activity.
"There's nothing else like this out there," said Mark Mulligan, vice president at Forrester Research. "Both parties have brought everything they have to offer to the table."
He said Virgin was smart to target the service at households where parents would pay the fee but it was likely that their children would make most use of it.
But by promising "a temporary suspension of internet access" for persistent offenders, Virgin appears to have gone further than any other ISP in acceding to the demands of the music industry.
Its success, he said, would depend on whether it won the backing of other music labels and gave unlimited access to their catalogues too. If it did then it might tempt many to defect from other services such as iTunes.
"If you have unlimited MP3s, as much as you could possibly want to get, why would anyone go anywhere else?" he asked.
But, he said, the two were taking a risk in launching the service.
"The UK digital market is littered with the corpses of failed music subscription services.
BPI boss Geoff Taylor welcomed the deal and said: "It is very encouraging to see an ISP and a record label working together as creative partners."
He added: "At the same time, the fact that Virgin Media will apply a graduated response system to tackle persistent illegal downloaders demonstrates that graduated response is a proportionate and workable way forward."
The Virgin/Universal deal was announced the day before the UK government releases the final version of the Digital Britain report put together by Lord Carter.
The report is widely expected to bestow new powers on communications watchdog Ofcom that will let it compel ISPs to do more to tackle file-sharing.
It is thought that one favoured solution to discourage persistent pirates will be to limit their internet connection speed.
Stephen Garrett from Kudos, the firm behind Spooks and Ashes to Ashes, warns that illegal file sharing could kill off quality TV shows
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