Another piece of Mayor Rahm Emanuel’s final budget fell into place Thursday: a new five-year agreement with AFSCME Council 31 with the same cost-saving health care reforms hammered out with the building trades.

Nine months ago — long before he pulled the plug on his re-election bid — Emanuel locked in labor peace with 21 percent of the city’s workforce through the 2019 election.

That agreement was expected to save Chicago taxpayers $12 million a year by 2021, thanks to health care reforms and increased employee contributions tied to the new five-year agreement.

But it’ll still cost the city $12.5 million this year and $57.8 million in the fifth and final year of the agreement. In part, that’s because it guarantees 52 percent of those 7,713 employees the prevailing wage paid to their counterparts in private industry.

Terms of the new five-year deal impacting 3,500 city employees represented by AFSCME Council 31 are virtually identical — minus the prevailing wage provision that does not apply to white-collar workers.

It includes a 10.5 percent pay raise over the next five years or 2.1 percent-each year.

It also includes a 1.5 percent increase in employee health insurance premiums by 2020 along with a $75 prescription deductible by 2021. And there’s a phased-in increase in the so-called “health care premium salary cap” from $90,000 to $130,000.

The cap is the portion of an employee’s annual salary to which the mandatory health care contribution applies. That contribution currently stands: at 1.29 percent or $43.88 every two weeks for single employees; 1.98 percent or $67.31 for couples and 2.48 percent or $83.95 per paycheck for employees with family coverage.

It will rise to 2.79 percent or $94.64 per paycheck for single employees; 3.48 percent or $118.14 for couples and 3.98 percent or $134.79 per paycheck for families. That’s an increase that still pales by comparison to the skyrocketing contributions faced by private sector employees.

The AFSCME contract still must be approved by the City Council.

That apparently explains why budget documents distributed to aldermen during closed-door briefings last week included a line for “collective bargaining agreement increases” with no specific cost.

Thanks to those reforms and more, overall city spending on the normally-spiraling cost of health care will be $30 million less in Emanuel’s final budget than it was when he took office in 2011.

In a statement released by the mayor’s office, Emanuel hailed the new AFSCME contract for the mutual respect it shows to Chicago taxpayers and city workers.

“This is another labor agreement that helps us better control the city’s health care costs and ensure the city’s fiscal stability for years to come,” Emanuel was quoted as saying.

“It stands as a testament of what’s possible when both sides roll up their sleeves and work together to find solutions that serve our common interests and help us reach our common goal of moving Chicago forward.”

AFSCME Council 31 spokesman Anders Lindall said the contract was “resoundingly ratified” on Wednesday night after more than a year of “challenging negotiations.”

“Our union represents more than 3,500 city employees who work in health clinics, libraries, police stations and countless other city worksites,” Lindall said in a statement.

“AFSCME members ensure that Chicagoans have clean water, safe buildings, sanitary restaurants and much more. This new five-year agreement provides family-sustaining wages and continued access to affordable health care for AFSCME-represented city workers.”

The new contract was announced shortly after members of the City Council’s Black Caucus were reassured during a closed-door budget briefing that the lame-duck mayor’s final budget would hold the line on taxes.

Emanuel plans to go out on a high note after pushing through a $2 billion avalanche of tax increases just to begin to solve Chicago’s $28 billion pension crisis.

“I’m hoping he doesn’t want to hang people out to dry. I’m assuming that he just doesn’t want to put people in a bad position in an election year,” said Ald. Roderick Sawyer (6th), chairman of the Black Caucus.

During Thursday’s briefing, aldermen were told that Emanuel plans to deliver his budget address on Oct. 17, one week later than originally planned.

Chief Financial Officer Carole Brown also told them that the mayor still has not decided whether to forge ahead with a controversial $10 billion pension borrowing tailor-made to minimize another punishing round of post-election tax increases.

Sawyer can only hope it’s full speed ahead.

“For the sake of knowing where you are and making sure we get things solid for the next couple of years, it goes a long way as opposed to not knowing how to pay this $220 million in [pension] increases next year,” he said.