For years, the New York Philharmonic and Lincoln Center have struggled to do something about the orchestra’s lackluster concert hall.

Plans came and went. Star architects signed on and signed off. The Philharmonic tried, disastrously, to return to its old home, Carnegie Hall. A $1.2 billion redevelopment gave Lincoln Center a sweeping makeover — but left the hall as is.

Then, in 2015, the entertainment mogul David Geffen restarted the project with a $100 million donation that gave the hall his name. But construction, which was originally to have started this year, was put off as logistical problems sent things back to the drawing board.

Now, officials say, the reconstruction of David Geffen Hall is finally about to happen — for real, this time. A new plan to transform the acoustically and aesthetically challenged auditorium into a more intimate, better sounding space was unveiled on Monday.

The project is expected to cost $550 million, of which $360 million has already been raised, Henry Timms, the new president of Lincoln Center, said. Perhaps most crucial is the plan to undertake the construction in phases, in order to limit the amount of time the Philharmonic is exiled — a major sticking point in earlier plans.

“We have to do it right this time,” said Deborah Borda, the president of the Philharmonic, during a recent walk-through of the hall. “And this, I think, is the plan to do it.”

Since it opened in 1962, the venue — first known as Philharmonic Hall, and then, after a major renovation in 1976, as Avery Fisher Hall — has been plagued by acoustical problems and complaints that its cavernous interior lacked intimacy. Over time it grew dowdy, if not plain ugly.

The new plan aims to tackle these issues. The stage will be pulled forward 25 feet (to what is currently Row J) to bring it closer to the audience, and new seating will wrap around the sides and back of the stage, reminiscent of the way it is configured for Lincoln Center’s Mostly Mozart concerts in the summer, as well as in many world-class halls built in the past 50 years.

The new space will have fewer than 2,200 seats, down from 2,738. The orchestra will be placed on stepped risers, so that back row percussionists will be as visible as the violinists up front, and a more steeply raked floor will also improve sightlines.

The upper tiers will be rebuilt, and seats there will be directed toward the stage — not set at right angles, as they are now, which forces audience members to look sideways. The walls will be resurfaced in order to improve the hall’s resonance, especially when it comes to bass frequencies.

“It will be a much more real, visceral reaction,” said Ms. Borda.

The plan seeks to strike a balance between the aspirational and the achievable. Earlier iterations had called for lowering the entire auditorium, which is currently on the second floor, to the level of the Lincoln Center plaza, which could have cost as much as $900 million, according to some estimates, and threatened to keep the Philharmonic out of its home for more than two full seasons.

That posed an existential threat to the orchestra, which would have had to persuade its dwindling subscriber base to follow it over years of wandering. New York City Opera’s decision to go dark for a season while its Lincoln Center home was renovated was later seen as one of the factors that eventually drove it into bankruptcy.

The new plan is more inside-the-box — quite literally, in the sense that the auditorium will maintain its existing footprint, and the exterior of the building, designed by Max Abramovitz, will remain intact. But officials stressed that the place would feel like new.

“It is being truly transformed and changed. It’s not putting paint on the walls,” said Ms. Borda, who returned to New York, largely in order to guide the renovation, after a 17-year run at the Los Angeles Philharmonic, which included opening its acclaimed Walt Disney Concert Hall.

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.

Ms. Tsien and Mr. Williams have designed high-profile projects including the Barnes Foundation museum in Philadelphia and the Asia Society’s Hong Kong center, and are currently working on Barack Obama’s presidential library in Chicago. The addition of the firm is the third significant architectural iteration of the project: Norman Foster was initially selected in 2005, followed a decade later by Thomas Heatherwick.

They will focus on making the hall’s public spaces — which can be confusing and off-putting, with long security-line bottlenecks — smoother and more comfortable.

“There are physical changes that are happening, but we’re also trying to change the emotional temperature,” said Ms. Tsien. “Because now the lobby space has all of the charm of an airport terminal.”

The relationship between the Philharmonic and Lincoln Center, its landlord, which also uses the hall for its own musical presentations and for corporate rentals, has sometimes been frosty. The Philharmonic’s short-lived attempt to merge with Carnegie Hall, in 2003, damaged the partnership, and some of Lincoln Center’s flashy earlier ideas for the Geffen Hall renovation were seen as unsuitable for a symphony orchestra. Both organizations have gone through management turnover as the project stalled.

But Mr. Timms and Ms. Borda said that relations have markedly improved, and that the current rethinking of the project was very much a collaboration, both in terms of planning and fund-raising, which they said would be done jointly going forward. The initial decision to rename the hall for a gift that will cover less than a fifth of the total cost has drawn criticism; officials said they expected to announce other naming gifts soon.

Mr. Timms said he hoped New York City would contribute money, as it has to other major cultural capital projects. He did not say how much he hoped to raise from the city, but said that Lincoln Center officials planned to “talk about the very many benefits this is going to have for New Yorkers of all backgrounds, and people traveling from around the world.”

There are still many decisions to be made, from the kind of wood that will line the walls of the auditorium to the color scheme of the new seats. But one thing is certain, Ms. Borda said as she surveyed the current interior: It won’t be this drab, cheerless brown.