LOS ANGELES — Kerry Brougher, the director of the Academy Museum of Motion Pictures, is leaving his position this summer, before a date has even been set for the museum’s opening.

After multiple construction delays and cost overruns, the $400 million museum — featuring a futuristic, spherical addition by Renzo Piano to the May Company building on Wilshire Boulevard — is expected to open sometime in 2020.

The museum board said in a statement that Mr. Brougher is leaving “to return to his roots in the art world,” without specifying his next step. The board added that “Kerry’s strong curatorial team will continue to work with us toward the Museum’s opening, and a search for a new Museum Director will begin shortly.”

Mr. Brougher, who will be given the title of founding director , noted that he has shepherded the project to an important stage. “We are just weeks away from completing construction of the buildings, ending the first phase of this project, and our collection has grown substantially,” he said in a statement.