Teachers who retired between 2009 and 2014 will receive the retroactive pay they were promised, even after a rush of retirees threatened to drain the city’s reserves for those payments.

An arbitrator’s decision, announced Monday, means that the city won’t have to set aside any more than the $180 million already apportioned in this year’s budget to pay the retirees. The United Federation of Teachers agreed to let the arbitrator come up with a package of cost-saving measures that would adjust the $5.5 billion contract agreement to find $60 million in savings to pay members who retired by July.

The decision, and the UFT’s response, represent a win for both the retirees and for the city. The city will not be responsible for the $60 million shortfall created when hundreds more opted for retirement this summer than last summer. The UFT’s new contract presented them with the option to receive years worth of back wages in one check, instead of receiving installments over many years, if they retired by July.

Once the disparity emerged, the union wanted the city to put up more money to pay the retirees, while the city argued such a move would be bad for taxpayers and pushed for the extra costs to be paid out of the labor agreement. Arbitrator Martin Scheinman agreed with the city.

It’s unclear where the $60 million in savings will come from, but Scheinman said in his decision that his adjustments would not be onerous.

“Out of a multi-year package costing billions of dollars, such modification shall not be difficult, and shall be relatively minor,” he wrote.

The retroactive pay dispute came after relatively peaceful negotiations between the city and the union over its long-expired contract earlier this year. Though former Mayor Michael Bloomberg had long insisted that the UFT’s members should not receive back pay for years worked without a new contract, the new administration found a way to provide the retroactive payments by denying raises to teachers who quit before the pact was ratified, delaying the bigger checks and raises and spreading them out until 2020.

“We were happy to work with the UFT to secure an agreement that provides workers with the fair contract they deserve while protecting NYC taxpayers,” said Amy Spitalnick, a spokesperson for the city’s budget department. “Today’s decision continues that fair and responsible pattern.‎