The past several years have been tumultuous for the academy. The #OscarsSoWhite controversy prompted a pledge in 2016 that the organization would double its female and minority membership by the end of next year, a move that has not been universally embraced by existing members. (This year’s 842 invitees were evenly divided between men and women, with people of color making up 29 percent of those invited.) This year’s awards show was marked by a series of decisions — hiring Kevin Hart as host, creating a popular best picture category, removing four other categories from the telecast — that were reversed after public outcries.

Mr. Rubin will be charged with unifying the splintered group while also managing its different initiatives. Those include the opening of the Academy Museum, which has been postponed until next year while the organization continues to raise the $388 million needed to fund it. In the latest wrinkle, the museum’s board announced Monday that the institution’s director, Kerry Brougher, would leave.

Mr. Rubin must also deal with the insurgence of streaming companies like Netflix, which often ignore the decades-old norms of theatrical distribution.

Mr. Bailey’s tenure was often chaotic. He presided over the lowest-rated Oscar telecast ever in 2018. He was accused of sexual harassment eight months into his stint, though the organization found the accusations had no merit.

In February, he became the face of efforts to shorten the awards show, in part by presenting four awards during commercial breaks, including the cinematography category. A group of 40 cinematographers and directors, including Spike Lee and Quentin Tarantino, sent an open letter to the academy, saying the proposal insulted “those of us who have devoted our lives and passions to our chosen profession.” The plan was scrapped before the show.