A TriBeCa complex once composed of low- and middle-income tenants is fast becoming a magnet for the well-heeled, as the allure of the former warehouse district is allowing for rents once unfathomable in the brick fortress-like 1,300-unit Independence Plaza.

The influx of wealthy renters into the complex, a series of three 39-story towers, is the latest chapter for TriBeCa, a neighborhood whose fortunes have soared over the past 20 years.

Independence Plaza left the rent-regulated Mitchell Lama program in 2003, immediately opening up a portion of its units to market rates. Since then, its 1970s-style red-brick-and-concrete facade and low ceiling heights have been trumped by the draw of a TriBeCa address and unobstructed views of the Hudson River, as rents for modest two-bedrooms have approached $5,000 a month. Just four years ago, under the rent regulations, tenants paid about one-fifth of current prices.

The complex was built in 1974, and reshaped the area by planting more than 3,000 new residents in the then-barren neighborhood. At the time, the neighborhood was dominated by storage sites, as trucks dropping off and picking up goods filled the roadways. The main source of activity was Washington Market, centered nearby on Duane Street, which was a former wholesale food bazaar.

Through the 1970s and 1980s, artistic types seeking large, cheap lofts were scattered through the cobbled streets of the neighborhood, which longtime residents describe as devoid of street life than compared to the activity today.

In the past 15 years, the neighborhood has seen an extraordinary number of conversions of former warehouses and industrial buildings into high-end lofts and condominiums. Stylish taverns and cafés have sprouted up throughout the area, and the ZIP code, 10013, is one of the wealthiest in the nation.

“TriBeCa is probably the most elite neighborhood in Manhattan today, so your demand is extraordinary,” a senior vice president at Halstead Property, Alan Pfeifer, said. Popular restaurants and a well-reputed school, P.S. 234, add to the draw of the area, Mr. Pfeifer said, attracting a mix of families and working professionals.

The shift in the neighborhood is almost hard to grasp, longtime residents say, as the area has become far more in demand than could have been imagined two decades ago.

“It’s a tremendous change — it’s unbelievable,” a TriBeCa resident since 1976 and co-owner of a string instrument repair shop, Judith Epstein, said. “It used to be, on the weekends, there was nobody here. The restaurants didn’t open, some of them, because there were just not people.”

An architect with BKSK Architects and longtime TriBeCa resident, Harry Kendall, said that in the mid-1990s, he was sought out to build an apartment building with concierge service, though at the time, he had strong concerns that there would ever be a demand for such amenities in the area.

“We wondered whether TriBeCa was ready for a building with a concierge,” Mr. Kendall said. “That quickly became clear that we were wrong.”

Tenants in Independence Plaza had generally been shielded from the soaring prices in the neighborhood due to its enrollment in the Mitchell Lama program. But since the landlord, Laurence Gluck, opted out of the program in 2003, units have gradually gone market-rate as existing tenants have left their apartments, bringing in a new demographic for the onetime low- and middle-income housing complex. Now, a sign on the building facing Greenwich Street advertises “luxury” rentals.

“The main thing is everyone is young and transitional — it’s very different from what our community was like here,” a 15-year resident, Elissa Kraus, said.

Most of the existing tenants after the buildings left Mitchell Lama did not have to pay marketrate rents, a vice president on the Independence Plaza North Tenant Association, Edmund Rosner, said. A government program subsidizes a large portion of their rents, while an agreement reached with the landlord limits the increases for others.

Tenants at the buildings are awaiting the decision of a lawsuit they filed against the building owner in which they alleged many of the building’s marketrate units need to be rent stabilized, Mr. Rosner said.