Financial giant State Street Corp. is vacating its two New York City office locations.

Executives at the Boston firm told New York staffers they won’t be returning to its Midtown Manhattan offices, according to people familiar with the matter. It expects to sublease the two offices near Rockefeller Center to other companies.

Many of State Street’s New York employees have worked remotely since the pandemic’s early days. The financial firm, like others, sent staffers to work from home when infections started surging across the country. Later, U.S. employees who needed an office could go into work if they followed safety protocols. The firm’s New York offices remained sparsely occupied.

In May, State Street told New York staffers to prepare for the closure of their offices. More than 500 employees across the firm’s custody bank and money-management businesses will be affected, some of the people said.

State Street is giving New York-based employees the option to work in other offices in New Jersey and Stamford, Conn. But the firm isn’t directing New York-based staffers to spend time in those offices, letting different groups across State Street determine the mix of in-person and remote work that suits them. State Street also secured some co-working space in Manhattan for those who want to use it.

A firm spokesman said State Street changed its real-estate strategy in New York to accommodate a hybrid workforce.

“We have taken a diligent look at our real-estate footprint in NYC,” spokesman Edward Patterson said. He added that the firm is “ensuring that our realty needs are in line with where our employees will be working.”

State Street’s pivot is part of a broader re-evaluation of New York City offices by financial firms.

Firms across business lines are questioning whether New York City’s costs, taxes and uncertain recovery from the pandemic make it worthwhile to maintain the same Manhattan office presence as before. In finance, some banks and other firms have ordered workers back to the office, while others have been slower to return to New York’s towers.

Goldman Sachs Group Inc., while maintaining its New York office, is planning to expand head count in West Palm Beach, Fla., by as much as several hundred in the near future, said a person familiar with the matter. Paul Singer’s hedge fund Elliott Investment Management LP moved its headquarters from New York to Florida at the start of 2021.

At stake is the office culture of financial firms and vitality of the nation’s financial capital.

“It’s certainly a wake-up call that we cannot take for granted New York’s position as the financial capital,” said Kathryn Wylde, chief executive of business group Partnership for New York City. “During the pandemic, people have learned they can work profitably from anywhere—and that’s a competitive threat to the concentration of talent in New York.”

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Adding to the New York dilemma, the spread of the Delta variant of the coronavirus has created logistical headaches for firms that need to make employees feel comfortable commuting and working in close quarters. Asset-management giant BlackRock Inc. recently delayed the formal date workers have to return to its New York headquarters by about a month, to October.

Even before the pandemic, some asset-management firms had been moving into smaller, lower-wage cities. Intense competition over the past decade forced many to take steps to reduce costs and protect profit margins.

AllianceBernstein Holding LP in 2018 decided to shift its headquarters from New York to Nashville, Tenn. The money manager cited lower state, city and property taxes as among reasons for the move. It plans to relocate 1,250 jobs to Nashville by 2024, and is 70% of the way toward that goal, a spokeswoman said. It will officially open its new Nashville office this fall.

State Street’s most well-known presence in New York is the “Fearless Girl” statue, a fixture outside the New York Stock Exchange on Wall Street. State Street’s exchange-traded funds are used by traders all around Wall Street, and the firm provides custody services for New York investment firms among others.

But a major chunk of its U.S. staff works out of the Greater Boston area.

Subleasing New York offices will help generate additional revenue for State Street, without the firm having to pay costs of breaking those leases. In the past year, low interest rates have eaten into custody banks’ bottom line. This year, the firm announced plans to cut 1,200 jobs, or 3% of its workforce, and to reduce office space for cost savings.

The State Street spokesman said there will be no changes to how it services clients in New York City and the surrounding area. He said the firm is committed to clients, business lines, corporate functions and staffers in the greater New York area, who include members of its executive leadership.

The “Fearless Girl” statue will remain on Wall Street.

Write to Dawn Lim at dawn.lim@wsj.com