The Hollywood Reporter said Spielberg is to begin shooting the movie next fall.
Day-Lewis has a pair of Oscars for his work in the films "There Will Be Blood" and "My Left Foot."
Liam Neeson was long attached to the Lincoln project, which would have reunited him with his "Schindlers List" director, but he recently bowed out because he said he was too old for the role. Neeson is 58 and Lincoln was 56 when he was assassinated in 1865.
Day-Lewis, 53, and Neeson appeared together in the 2002 period picture "Gangs of New York."
"Daniel Day-Lewis would have always been counted as one of the greatest of actors, were he from the silent era, the golden age of film or even some time in cinema's distant future," the entertainment industry trade newspaper quoted Spielberg as saying. "I am grateful and inspired that our paths will finally cross with Lincoln."
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