Established in 2007 by former Channel 4 and Vodafone executives Michael Comish and Adrian Letts, Blinkbox now offers more than 9,000 TV shows and films to rent or buy.
The VOD site has around 2 million users and is also available on a range of devices, including tablet computers, Sony's PS3 and connected TVs, such as Samsung Smart TVs.
Tesco has acquired an 80% stake in Blinkbox from Eden Ventures and Nordic Venture Partners, and intends to use the company to bolster its digital entertainment offering. Financial terms of the deal were not disclosed.
Richard Brasher, Tesco's UK chief executive, said that the supermarket chain is committed to providing customers with a range of entertainment products, including DVDs, digital downloads and streaming services.
"We want to allow [consumers] to decide how they access entertainment content, and on which devices - whether it's on PC, TV or tablet," he said.
"The acquisition of Blinkbox, together with a range of other services currently in development, means we can link physical purchase of a product to the building of digital collections in a new and seamless way.
"Working with the Blinkbox team and our content partners, we will bring these compelling propositions to life for our customers."
Blinkbox chief executive Michael Comish added: "We are pleased that our partnership with Tesco allows us to bring the best in entertainment from our library of over 9,000 titles to even more people across the UK. It's a hugely exciting time, looking at how accessible entertainment is becoming for consumers.
"This partnership represents another step forward, bringing the leading movie streaming service together with the UK's biggest retailer."
Blinkbox is also part of a group of content of content partners working with YouView, the BBC-backed IPTV platform launching in the UK next year.