The purchase of Mobcast, founded by Bravo Two Zero writer McNab in 2007 with Tony Lynch, marks the latest expansion of Tesco's digital entertainment offering.
This follows the acquisition of the TV and movie downloads company Blinkbox in 2011 and a deal to buy the We7 digital music streaming service this year.
Tesco said that buying the Mobcast platform will "offer our customers even more choice in how they buy and enjoy books".
Mobcast is a digital book retail platform that has a catalogue of more than 130,000 books which can be bought and read on smartphones, tablets and selected eReaders.
Using cloud technology, Mobcast customers can store their books on remote servers and then access them on multiple devices.
Buying Mobcast gives Tesco a ready-made eBooks operation, as the 5-year-old company already has agreements with all the major publishers, along with mobile network operators, equipment manufacturers and retailers.
Michael Comish - the founder of Blinkbox who is now chief executive of Tesco Digital Entertainment - said: "We want our customers to have the widest choice in digital entertainment.
"We are already one of the UK's largest booksellers and Mobcast will help us offer even more choice for the large and growing number of customers who want to buy and enjoy books on their digital devices whenever and wherever they want."
Sales of electronic books have rocketed since Amazon's Kindle devices and Apple's iPad tablet hit the market.
The Publishers Association said earlier in the year that digital sales increased 366% last year to £92m. That is expected to increase again this year due to the popularity of erotic novel Fifty Shades of Grey.
Online retail giant Amazon now sells 114 eBooks for every 100 hardback and paperback books sold on its website.
McNab said that the Tesco deal will ensure that Mobcast is available to "as many people as possible".
"As an author I always thought the ability to carry your library around and read on all your personal devices would be a huge benefit to all," he said.
"We have developed a product that makes this possible, and being acquired by Tesco ensures that this original vision will be available to as many people as possible."
Mobcast chief executive Lynch added: "Since we launched Mobcast in 2007, we have been passionate about innovation, the digital book market and allowing customers to read across their devices.
"We are delighted the products that Mobcast has developed will now be used to introduce the joys of eBook reading to more book lovers in the UK."