Cooper, an Academy Award winner for his work in "Adaptation," will play Antonio with former rocker Carney as Ferdinand.
The duo join the previously announced Academy Award winner Helen Mirren as Prospera (a gender-bending take on the role of Prospero, which is usually played by a man), Oscar winner Jeremy Irons, Djimon Hounsou, Russell Brand, Alfred Molina, Ben Whishaw and Felicity Jones.
The film, according to the industry paper, will "center around Prospera, her daughter Miranda (Jones) and a shipwrecked crew full of Prospera's enemies."
The Miramax motion picture will begin shooting next week in Hawaii.
Tony Award winner Julie Taymor is best known for designing and directing the Disney hit The Lion King. Her film credits include "Titus" and "Frida." She is currently at work on a Broadway musical version of Spider-Man.