NI Group's agreement covers rights to show clips of all 380 Premier League football matches online, as well as exclusive rights to near-live clips of games on mobile devices. The rights were previously held by Yahoo and ESPN respectively.
NI is part of Rupert Murdoch's News Corporation, which also owns 39.1% of Sky. Sky has agreed its own wide-ranging deal this week to Premier League highlights on television.
Starting in August 2013 in time for the next football season, NI's deal means that it can present up to eight 30-second clips during live matches on smartphones and tablets, although that excludes Saturday 3pm kick-offs, which the Premier League protects in order to boost attendance at stadiums.
The agreement also allows 60-second clips of each Premier League game to be made available via the three papers' digital platforms for a week after match-day.
Financial terms of the deal have not been officially announced, but The Guardian claims that it is worth more than £20m, citing "a source with knowledge of the bidding process".
NI said that subscribers will be able to access the video clips on the new Sun tablet app, due to launch in the next few months, along with the Sun's smartphone app and via The Times and The Sunday Times digital products.
Mike Darcey, the former Sky chief operating officer who was recently appointed News International chief executive, said that the deal is a "major breakthrough" for the company, and also part of its use of cutting-edge technology to "transform the experience we are offering our subscribers".
Premier League stars Robin van Persie and Eden Hazard
"They [subscribers] will now have access to the most compelling moments in the most competitive football league in the world at a time, place and format that suits them," he said.
"In a rapidly changing industry, this is an unprecedented moment and a testament to the pioneering attitude of which we can be proud. Once again we are leading the way with innovative technology, drawing on our journalistic heritage and our unrivalled world-class content."
NI Group's Premier League deal marks the first major move by the publisher since it became part of New News Corporation, the publishing business of Rupert Murdoch's News Corp that has been split from the entertainment division, Fox Group.
Robert Thomson, a former editor of The Times who was appointed to run News Corporation, said of the deal: "Smartphones are only going to get smarter and we have to be just as clever in creating content and finessing the format.
"With an eye toward the virtuosity of video, the new News Corp will be focused on complementary content, repurposing our expertise across platforms and across the globe.
"The confluence of digital technology and football is one of the great meeting places of the modern world, so this is quite a moment for the company. We are practising our goal celebration."