The actor will join Ben Whishaw, Halle Berry and Tom Hanks for the project, according to The Hollywood Reporter.
David Mitchell's sci-fi influenced novel follows several interconnected characters in different continents over two centuries. Each actor will reportedly take on multiple roles.
The script will be penned by Run Lola Run writer Tom Twyker, who said in 2009 that it will move from "from Melvillean high-seas drama to California noir and dystopian fantasy".
Weaving has already confirmed his return to prequel The Hobbit after starring in the three Lord of the Rings films.