Sky Player TV offers live TV and video-on-demand and can be accessed through a PC or Mac.
It marks the first time that consumers can access pay TV content online without the need to subscribe to an existing TV-based service.
Subscription packages for Sky Player TV range in price from £15 for the Entertainment Pack through to £34 for the addition of all of the Sky Sports family of channels.
The Entertainment Pack initially offers access to Disney Channel, British Eurosport, National Geographic Channel, Sky News, and Sky Sports News.
Customers can add to their Entertainment Pack by subscribing to one or both of the Sky Sports Packs to access Sky Sports 1, 2, 3, and Sky Sports Xtra.
Later in December, MTV Networks UK & Ireland's channels MTV ONE, Nickelodeon and Nick Jr will join the Entertainment Pack. Further channel launches, including additions from the rest of the Sky channel portfolio, will follow in the New Year.
The Sky Player TV service was developed in conjunction with Microsoft using its Silverlight and PlayReady technologies.
Mike Darcey, chief operating officer at BSkyB, said: "We want to give customers as much choice as possible not just in what they watch, but in how they watch it.
"Sky Player TV recognises that for some, the computer screen is now the preferred screen through which to watch TV.
"In developing a standalone subscription to a secure online platform, we are responding to the diverse needs of today's customers."