Mobcast, set up by McNab and chief executive Tony Lynch in 2007, provides a platform for companies to sell e-books and currently works with mobile network Orange.
Tesco bought the company, which has its headquarters in the East London Tech City area, for £4.5 million to strengthen its own digital entertainment offer.
The country's biggest grocer bought the movie and television streaming service blinkbox last year and personalised internet radio service WE7 in June.
McNab said: "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. We have developed a product that makes this possible, and being acquired by Tesco ensures this original vision will be available to as many people as possible."
Mobcast has a catalogue of more than 130,000 of the UK's most popular titles which can be bought and read on smartphones, tablets and e-readers.
The company offers an online cloud-based service that lets customers build up an e-book library collection without being locked into one single device.