The film - about a man hunting a group of dangerous criminals across the Australian desert in the future - will be presented in the Official Selection: Out of Competition.
Writer and director David Michod (best known for his critically acclaimed film Animal Kingdom) will be in attendance at the film's international debut.
"David Michod has created an extraordinary film," Roadshow Films Managing Directed Joel Pearlman said in a statement.
"We congratulate him, the producers, cast and crew on this incredible achievement.
"Cannes remains the leading light among film festivals and this is a well deserved honour for The Rover."
Michod will be joined in Cannes by Pearce and Pattinson, best known for the Twilight movies but also recently showing his dramatic skills in David Cronenberg's Cosmopolis.
It has also recently been announced Michod will write and direct the forthcoming production The Operators, to be produced by and starring Brad Pitt.