3 World Trade Center, nearly the size of the Empire State Building, is 20% leased, leaving a big space to fill in a market that is only gradually improving. Bloomberg News

After more than a year of uncertainty, a third tower at the World Trade Center site appears poised to rise thanks to an unlikely catalyst: a turnaround in the market for municipal bonds.

Developer Larry Silverstein is planning to sell $1.6 billion of tax-exempt bonds to finance 3 World Trade Center as soon as next week, a move that would give the 1,170-foot tall New York tower the funding to move forward.

If the sale proves successful, the 2.5 million square-foot tower would be the latest byproduct of investors’ hunt for yield. With Treasury yields pushing lower, investors have been searching for investments that generate better returns, even if the risks are greater, benefiting everything from Silicon Valley startups to toll roads.

Executives involved with the tower began looking for money last year and determined there wasn’t enough investor demand. But a rally in the muni-bond market has given them confidence the bonds will sell and the tower can rise on the 16-acre site.

The improvement in the muni market “has created real optimism about this transaction,” said Janno Lieber, who oversees World Trade Center development for Silverstein Properties Inc.

Limited muni-bond supply due to reduced borrowing by cities and states helped push muni-bond rates to a 2014 low of 2.19% last week, from 3.3% in January, according to the S&P Municipal Bond Index. Bond yields move in the opposite direction of prices.

The 3 World Trade Center bonds would be at a higher rate—expected to be between 5% and 6%—but still below what traditional lenders charge for construction debt. Adding to their appeal: The tower’s bonds are tax-exempt because of congressional action related to the site’s rebuilding.

Still, the bonds aren’t without risk. The 3 World Trade property, nearly the size of the Empire State Building, is just 20% leased, leaving a large space to be filled in an office market that is only gradually improving.

“Rates are so low that people are stretching for yield, which often means going down the credit scale,” said Howard Cure, head of municipal research at Evercore Wealth Management LLC, which oversees about $5.4 billion.

Silverstein has been planning the tower for years, although construction was halted at eight stories until the developer locked in a tenant and financing, based on the terms of a 2010 government-aid agreement.

The developer secured its tenant last year when advertising firm GroupM, a division of WPP, agreed to take 515,000 square feet in the base of the building.

But when Silverstein looked at its options for financing, it saw that the interest payments on municipal debt would be too high. Meanwhile, banks weren’t willing to make a loan for a building with so much vacancy. Lenders have remained relatively conservative since the downturn, and typically lend only for buildings with significant leasing agreements in place.

“The banks are not in a position to take that risk yet,” Christopher Haynes, president of loan-advisory firm Broadacre Financial Corp., said of construction loans for office towers without tenants. “I just don’t think the market’s there.”

Silverstein initially went to the Port Authority of New York and New Jersey—which owns the 16-acre site—and asked the agency to back most of the debt. While agency officials were supportive, its board rejected the request in the early summer, leading Mr. Silverstein to turn back to the bond market.

The result was encouraging. Silverstein’s bankers at Goldman Sachs Group Inc. and other advisers told the developer the deal might be able to work based on the terms of the 2010 aid package, in which the Port Authority would cover the first $210 million of shortfalls to investors.

Aided further by a noticeable uptick in the lower-Manhattan leasing market, Silverstein put in $50 million of equity and the bankers began to seek investors.

In recent weeks, bond managers have toured the site, walking through the under-construction concourse below the tower while strolling by 4 World Trade Center, the recently completed tower that also was built by Silverstein, and 7 World Trade Center, Silverstein’s fully leased tower built in 2006.

For the investors, the risk lies largely with the state of the Manhattan office market. While a number of companies like Time Inc. recently have been opting to move from Midtown to lower Manhattan, any slowdown in the economy could quickly put a halt to pricey moves and cause companies to stay in place.

It isn’t clear how much time Silverstein believes the building will take to lease up fully. But an independent appraisal provided to bond investors projects the tower will be leased by 2021, three years after it is completed, assuming it secures financing this fall.

—Andrew Tangel contributed to this article.

Write to Eliot Brown at eliot.brown@wsj.com and Aaron Kuriloff at Aaron.Kuriloff@wsj.com