This follows a deal with record label BMG, which has agreed to offer videos from its library of artists, including Justin Timberlake, Outkast, Christina Aguilera, Britney Spears and Dido.
Users with 3's video hand-sets will be able to either download or stream videos for £1.50 each or buy an Unlimited Content Add-On for £10 a month to gain access to all of 3's premium content.
The move places the UK at the forefront of the mobile music market, alongside Italy and Australia, where 3 also runs music download services.
The deal with BMG will enable 3 to offer the latest video releases to users at the same time that they are launched on music video TV channels.
However, the company is also hoping to seal deals with artists and their record labels to win 'first play' rights.
A spokesperson for 3 said: "Videos are usually released six weeks before the relevant single goes on sale - they will now go to 3 and MTV at the same time, so about four to six weeks before release. We are also dealing with BMG on a case-by-case basis (for exclusive releases)."
The network's spokesperson added it expects most 3 users to view videos on their mobile before arriving home to watch them on TV.
"It is a service that is ideal for filling users' time when they are waiting for a train, for example, or to show their friends," the spokesperson said.
The new music service will be accompanied by the launch of a new area on 3's content pages, offering the latest releases in a 'new this week' section, along with a video chart of the most popular downloads.
Gareth Jones, chief operating officer at 3, commented: "For the first time, fans will be able to see full-length music videos on their phone before they see them anywhere else."
Tim Bowen, chairman of BMG UK & Ireland, added: "3's new technology develops on from ringtones by giving a brand new must-have music application to consumers on the move."