According to The Hollywood Reporter, the two actors join previously announced cast members Cillian Murphy and Emily Blunt in the film.
The Universal Pictures project is a biopic of J Robert Oppenheimer, the theoretical physicist remembered as one of the fathers of the atom bomb.
Oppenheimer will be the first time that Robert Downey Jr, the star of many Marvel Cinematic Universe (MCU) movies, and Oscar winner Matt Damon will work with Christopher Nolan.
The details of their roles have been kept under wraps.
Murphy is set to star as J Robert Oppenheimer and Emily Blunt as his wife Katherine.
Cillian Murphy and the director have worked on his three previous films Batman Begins, Inception and Dunkirk.
Oppenheimer is based on the Pulitzer Prize-winning book American Prometheus: The Triumph and Tragedy of J Robert Oppenheimer by Kai Bird and Martin J Sherwin.
Christopher Nolan will write and direct the film, while his creative partner and wife Emma Thomas will produce with Charles Roven of Atlas Entertainment.
The studio has described the film as an “epic thriller that thrusts audiences into the pulse-pounding paradox of the enigmatic man who must risk destroying the world in order to save it”.
Nolan’s last film was Tenet, the 2020 globetrotting espionage film starring John David Washington, Robert Pattinson, Kenneth Branagh and Elizabeth Debicki, among others.
Oppenheimer is slated to be released in theatres on July 21, 2023.