Connected Red Button, as the BBC is calling it, is a reinvention of the corporation's popular Red Button offering that provides additional TV, radio and online content through select digital TV platforms.
The new service will first roll out on Virgin Media's TiVo platform under a partnership agreed between Virgin and the BBC to create next-generation TV experiences.
It allows users to watch programmes from the BBC children's channels, BBC Three and BBC Four at any time - day or night - even if the channel is off-air. They can also catch up on previous episodes of BBC shows.
Following the huge success of the Red Button coverage during the London 2012 Olympics, BBC Connected Red Button will offer additional content around sporting events, including more live streams, video clips and data.
Users can also browse the latest news and weather headlines and video clips at the touch of a button.
BBC Connected Red Button arrives in around 1.2 million Virgin Media TiVo homes today, and then will expand to other internet-connected TVs over "the coming months".
The corporation said that the service will redefine how audiences watch, engage with and interact with BBC content on their TV. Additional functionality and features will be added to the service over time, it added.
Red Button has been offered by the BBC for more than 13 years, helping viewers get closer to the action at major events like Glastonbury, Wimbledon and Formula 1 races.
The service launched in September 1999 as BBC Text, but was later relaunched as BBCi in 2001 and then became BBC Red Button in late 2008.
It now attracts an audience of around 20m per month, peaking during this summer's Olympic Games, when 24.2m viewers watched up to 24 live video streams of events via the service.
The BBC wants to gear the platform for the future, as it is expected that there will be almost 22m internet-compatible TVs in the UK by 2016.
At that time, around 50% of British homes are predicted to have a web-connectable TV as their primary living room set.
BBC programmes and on-demand general manager Daniel Danker said that today's launch brings "the internet together with live TV, while making the technology completely invisible".
"This is Red Button reinvented, and the beginning of the exciting future of television," he said.
Victoria Jaye, the BBC's head of IPTV & TV online content, said that getting connected would "add value" to the TV experience.
"With BBC Connected Red Button, we're starting with the TV audience who love our broadcast output and we're curating online content on the big screen in ways that add value to their TV viewing," she said. "The audience can sit back and relax - the internet just made TV better."
Virgin Media's executive director of digital entertainment Cindy Rose added: "The BBC understands as passionately as we do how important connected television is for home entertainment.
"We're delighted the BBC is working with us to launch another milestone in interactive services. Our commitment to this partnership of innovation means Virgin Media TiVo customers are the first to experience the latest interactive services at the press of a button."
Sky said that it has not yet entered negotiations with the BBC over bringing the connected Red Button service to its satellite platform, but is keeping an eye on the situation.
"We have not yet entered into discussions with the BBC about Red Button video services streamed over IP, but we will keep the situation under review," a Sky spokesperson said.
"In the meantime, the BBC will continue to support some satellite-based Red Button functionality for major shows and events.
"For popular events, such as Wimbledon and the Olympics, additional video streams broadcast via satellite would enable the BBC - and other broadcasters - to continue to cater to all 10 million Sky homes."