The decision to honour Polanski’s An Officer and a Spy has angered feminist groups and led to calls for a boycott.
The Polish-French director has been wanted in the US for the statutory rape of a 13-year-old girl since the 1970s.
Hundreds of actors, producers and directors have also called for reform.
In an open letter this week, they denounced “dysfunction” at the César Academy and opacity in its management.
The César Academy’s decision to step down en masse came as a shock ahead of the glittering 45th awards ceremony in Paris, which is to be held on 28 February.
In a statement on Thursday night, the academy said the board had “unanimously decided to resign” to “honour those men and women who made cinema happen in 2019, to find calm and ensure that the festival of film remains just that, a festival”.
“This collective decision will allow complete renewal of the board,” it added.
A general meeting is set to be held after this month’s ceremony to elect a new board, which will look at implementing reforms and modernising the institution.
Culture Minister Franck Riester said the César Academy must operate democratically, in the spirit of “openness, transparency, parity and diversity”.
What’s the background?
The César Academy has faced controversy in recent months.
Many called for a boycott when Polanski’s film An Officer and a Spy, or J’accuse in French, received 12 award nominations. The Polish-French director fled the US after his rape conviction in the 1970s, and has since faced other accusations of sexual assault.
“We’re in shock that Roman Polanski, who’s accused by several women of paedophile rape crimes, is yet again hailed by French cinema,” said Céline Piques, spokeswoman for French feminist organisation Osez le Féminisme (Dare to be Feminist).
France’s equality minister, Marlène Schiappa, also condemned the decision to nominate Polanski’s film.
While praising the academy’s efforts to recognise France’s MeToo movement, Ms Schiappa said she found it “impossible that a hall gets up and applauds the film of a man accused of rape several times”.
But the Césars defended the nominations, arguing that the body “should not take moral positions” in giving awards.
Polanski himself told Paris Match in December that he had tried to distance himself from the calls for a boycott of his film. “For years people have tried to make me out as a monster. I’m used to the slander and I’ve grown a thick skin, which is as hard as a shell,” he said.