The Bronx Museum of the Arts, whose attendance has quadrupled since it instituted free admission in 2012, announced Wednesday that it had started a $25 million capital campaign to renovate and expand its building along the Grand Concourse and to establish an endowment for the first time.

The building project, which has already received around $7 million from the mayor’s office, the New York City Council and the Bronx borough president’s office, will be overseen by the architect Monica Ponce de Leon, dean of the School of Architecture at Princeton University and a co-curator of the United States pavilion for the 15th Venice Biennale of Architecture, which opens to the public on Saturday.

The museum, founded in 1971, last expanded in 2006 with a widely admired $19 million north-wing addition designed by the Miami-based firm Arquitectonica. But the museum’s various parts have never been knit together well and some spaces are awkward and underused, said Holly Block, its director. So the rebuilding, which will add some exhibition room and create a new glassed-in space for educational and public programs at the corner of 165th Street and the Grand Concourse, will make the museum feel like a visual and architectural whole for the first time, she said.

“We’ve been very secret about this, because we didn’t want it to be public until we were sure,” Ms. Block said. “It’s so great for the Bronx to have any kind of capital projects like this. And we’ve been waiting a very long time.”