The newspapers span three centuries and include 52,000 local, national and international titles.
The newspapers are currently in a store in Colindale, north London, and are used by 30,000 researchers every year.
The British Library said putting the papers online would help improve access to the information.
The British Library's chief executive, Dame Lynne Brindley, said: "Mass digitisation unlocks the riches of our newspaper collections by making them available online to users across the UK and around the world.
"By making these pages fully searchable we will transform a research process which previously relied on scrolling through page after page of microfilm or print."
The plan is to digitise a minimum of four million newspaper pages over the first two years.
Over the course of the 10-year agreement, up to 40 million pages should be put online.
Brightsolid is a subsidiary of the Dundee publisher DC Thomson and owns findymypast.co.uk and Friends Reunited.
The firm will digitise content from the British Newspaper Library, which it will then make available online via a paid-for website.
Chris van der Kuyl, chief executive of Brightsolid, said: "Digitisation will mean that those people who haven't previously been able to access the physical resource will now be able to access it from anywhere at any time."
He added: "It will also offer a unique insight into major events and key periods of historical interest."