The construction schedule , which relies on having some components built ahead of time, has been designed to limit disruption to the orchestra. The hall will close in May 2022, shortly before the end of the Philharmonic’s regular subscription season, and reopen that November, two months after its season usually begins. The orchestra will then play a slightly abbreviated season in the unfinished hall from its new stage, which will have been moved forward.

The hall will close again in May 2023 for nearly a year to finish the work — during which time the orchestra plans to perform at Carnegie Hall, New York City Center, elsewhere in the city and on tour.

The rebuilt Geffen Hall is scheduled to open in March 2024, though it has not been unusual for major concert halls, including the glamorous new Elbphilharmonie in Hamburg, to face delays and cost overruns. Ms. Borda said she expected the Philharmonic’s music director, Jaap van Zweden, to preside over the reopening — an early indication that she anticipates extending his current five-year contract, which is up in 2023.

Mr. Geffen, who had expressed frustration at some of the earlier setbacks, said he was pleased. “I hear the plans are great and can’t wait to see them,” he said in an email. “New York deserves a great concert hall.”

Mr. Timms of Lincoln Center said that he also saw the project as an opportunity “to give people deep connections with not just the music but with each other” and “to think quite carefully about how we connect with the outside world.”

The hall’s public spaces are being revamped with that in mind. The redesign calls for moving the box office and doubling the size of the lobby; adding a casual bistro and more bars and restrooms; building a Lincoln Center welcome space; and transforming the corner of the building at the busy intersection of 65th Street and Broadway — currently office space hidden behind curtains — into a public-facing “Sidewalk Studio” for classes, lectures and small performances. The building’s 65th Street facade is intended to become a large-scale canvas for site-specific artworks.