The five-year pact will come up for a vote Thursday at the monthly meeting of PHA's board of commissioners.
The U.S. Department of Housing and Urban Development, which provides most of PHA's funding, also must endorse the agreement.
Jeremiah said there already was broad support from Mayor Nutter, city officials, and HUD leaders.
The agreement covers contracts of more than $5 million. It does not cover members of the building trades who are employees of PHA and who maintain existing properties.
"This is a very, very good negotiated agreement," said Pat Eiding, secretary-treasurer of the Building and Construction Trades Council of Philadelphia.
Eiding, who also is president of the Philadelphia Council of the AFL-CIO, said the agreement "didn't happen without a whole lot of consternation and meetings." But he added that some of the 14 unions represented by the building council "haven't had a hell of a lot of work in the last couple of years."
Eiding said much of the residential construction in the city was being done by nonunion contractors.
The agreement, Eiding said, is "probably going to go down in history as a memorable moment."
He said it was difficult to calculate how much PHA would save. The dollar sum of the wage reductions, he added, will vary from union to union, but will remain at 20 percent of total compensation.
In affordable housing, PHA is the main player in the city.
"To be able to get such a significant change in rates could be dramatic in terms of the number of affordable units they can build," City Council President Darrell L. Clarke said.
Clarke is leading a drive to add 2,000 units of affordable housing in the city. He said the building trades approached him to see how they could help.
Jeremiah said that with existing labor expenses, it can cost $300,000 for PHA to build a house. If PHA sells the unit as affordable housing to a lower-income homeowner, it must subsidize the cost.
In the next five years, PHA expects to spend more than $280 million on new construction. That includes a redevelopment of the area around the Blumberg housing project in North Philadelphia and a new headquarters building planned for Ridge Avenue in the Sharswood neighborhood.
Eiding acknowledged that giving PHA a discount may lead other developers to ask for the same. "I hope it does," he said, adding that in return, the unions would want long-term employment commitments.
"When you get into residential building, some trades may only have a day or two on a job," Eiding said. "The value is, you're going to do many of them."
Jeremiah said the labor agreement would allow the authority to do more with a shrinking $371 million budget.
PHA is not required to hire union contractors. But with the agreement, the agency would pledge to engage only contractors who hire union laborers, carpenters, painters, and other workers.
"It ensures that their members have jobs for the long term," Jeremiah said. "And we have the ability to build more units."
As part of the agreement, contractors for PHA must pledge to set aside 25 percent of the jobs for public-housing residents. They must also ensure that 20 percent of the subcontractors they hire are women or minorities.
The agreement eases tense relations between Jeremiah and the building trades. When he became acting executive director of the authority two years ago, Jeremiah clashed with labor leaders over a decision to eliminate provisional jobs for the construction trades. The move, Jeremiah said at the time, would save the agency millions by getting rid of overpaid temporary painters, carpenters, and laborers.