Joshua Bright for The New York Times

It took 14 speakers and an 11-page news release on Monday to spread the news that city officials had struck a deal for New York University to create a school of applied science in Downtown Brooklyn.

The agreement, which has been in the works for months, would end years of debate about what to do with the old headquarters of the city’s transit authority at 370 Jay Street. The Metropolitan Transportation Authority had largely abandoned the 61-year-old building, transferring many of its occupants to other offices in Manhattan.

To move the transit authority’s equipment and remaining employees out, N.Y.U. promised to pay $50 million of the relocation costs. It also agreed to pay as much as $10 million to move the New York Police Department out of some space it occupies in the building.

In exchange, the city agreed to rent the building for $1 a year to N.Y.U., a private university with an endowment of $2.5 billion. The city also offered a $15 million package of breaks on taxes and energy costs and possibly some cash.

Asked why public property would essentially be turned over to a private university that charges more than $40,000 a year for tuition, Mayor Michael R. Bloomberg said that the public would benefit from having the school built in the hub of Brooklyn.

N.Y.U. “is putting their cash on the line,” the mayor said. “We should be saying thank you to them.”

And many elected officials and business leaders lined up behind the mayor to do just that. As he spoke at a lectern in the lobby of the Polytechnic Institute of New York University’s building across from 370 Jay Street, he was flanked by nearly three dozen people who were given credit for having helped in some way.

Several of them were leaders of universities that formed a consortium to bid in the competition that the city’s Economic Development Corporation set up to establish a graduate school of applied science. Mr. Bloomberg saw that project as a solution to the city’s inability to compete with Silicon Valley for engineering and science talent.

Cornell University, in partnership with the Technion school in Israel, won the competition with a plan to build a $2 billion campus on Roosevelt Island. But the group led by N.Y.U. forged ahead with its plan to create a smaller school in Brooklyn. The other schools involved are NYU-Poly, the City University of New York, Carnegie Mellon University, the University of Warwick, the University of Toronto and the Indian Institute of Technology, Bombay.

N.Y.U. officials did not say how much they expected to spend on the venture. But John Beckman, a spokesman for N.Y.U., said the consortium would spend as much as $750 per square foot to gut and renovate the building — if it determined that the project was feasible. The group plans to create the center even if it decides that the transit agency’s building is not suitable, he said.

On Monday, a notice taped to the wall of the building’s lobby warned entrants that work was under way to remove asbestos. Outside, the building’s lower facade was obscured from view by scaffolding that has been in place for years.

Marty Markowitz, the always-on borough president of Brooklyn, proclaimed that “370 Jay Street will no longer be an eyesore to Downtown Brooklyn.”

But officials of the Transport Workers Union were not so thrilled when they heard about the deal. “It’s a win-win for everyone but transit riders, who are still feeling the horrendous effects of the massive service cuts the M.T.A. engaged in in 2010,” said John Samuelsen, president of Local 100, which represents 40,000 transit workers.

Mr. Samuelsen said the transit authority should have renovated the Jay Street building instead of moving into more expensive quarters in Lower Manhattan and reducing service. But transit officials, who approved the transaction with N.Y.U. at a meeting on Monday, said it would have cost more than $200 million to modernize the building in Brooklyn.

City officials provided lofty estimates of the benefits the city would reap from the school, which is expected to start up next year in rented space nearby and move into the building in 2017. Mr. Bloomberg said the project would yield more than 2,000 construction jobs and that over 30 years, it would generate more than $5.5 billion in economic activity and $597 million in tax revenue.

If all that comes true, the time and effort expended to wrangle the deal to fruition will have been worthwhile, said Daniel L. Squadron, a Democratic state senator.

“With the number of people up here and the amount of time this took, we could have built a new building,” Mr. Squadron said, gesturing toward the assemblage standing two and three deep behind him. “Rarely has one building been so hard to make work.”