The series will explore how patent clerk Einstein could not get a teaching job or doctorate in his early life yet managed to go on to develop the theory of relativity.
The young scientist will be played by Johnny Flynn, Hollywood Reporter said.
Genius will be National Geographic’s first scripted series.
Variety reported in April that Ron Howard would direct the first episode of the drama, which is based on Walter Isaacson’s book Einstein: His Life and Universe.
Each episode will look at Einstein’s complex personal relationships as well as his scientific achievements.
The series is expected to be shown in 171 countries and 45 languages.
Oscar-winning director Howard, who won two Oscars for A Beautiful Mind and was nominated for two for Frost/Nixon, said: “National Geographic’s unwavering commitment to excellence and their support and passion for this project has helped us attract talent such as Geoffrey and Johnny.”
Rush previously starred in HBO film The Life and Death of Peter Sellers and won an Oscar for 1996’s Shine. He was also nominated for The King’s Speech, Quills and Shakespeare in Love.
Flynn was nominated in 2012 for an Olivier for the play Jerusalem and also for London Newcomer of the Year at the What’s On Stage Awards.
Rush’s decision to star in the series follows on from the news earlier this month that fellow Oscar winners Robert De Niro and Julianne Moore are to star in a TV series directed by David O Russell.
BBC