Armstrong, whose name and celebrity status helped build a multimillion dollar cancer foundation, admitted on Thursday that he used performance-enhancing drugs to win a record seven consecutive Tour de France championships after denying doping allegations for years.
The forthcoming book, "Cycle of Lies: The Fall of Lance Armstrong" by New York Times reporter Juliet Macur, traces his recovery from cancer, inspirational return to cycling, and his fall to disgraced ex-champion.
The book is set for a June publication by HarperCollins.
Neither Paramount nor Bad Robot would comment on the deal, which was first reported on the Deadline Hollywood entertainment site.
Abrams, the producer and director of the forthcoming science-fiction thriller film "Star Trek into Darkness," co-founded Bad Robot with producer Bryan Burk.
Paramount will distribute the big-budget "Star Trek," which is scheduled for release in May. Paramount has distributed other Abrams-produced films, including 2011's "Mission: Impossible - Ghost Protocol," starring Tom Cruise.
Paramount Pictures is a subsidiary of Viacom Inc and HarperCollins is owned by News Corp.
(Reporting by Eric Kelsey; Editing by Lisa Shumaker)