The city has agreed to a last-minute change to its teacher evaluation system that could reduce the number of required classroom observations for tens of thousands of teachers this year.

Teachers who have been rated “effective” now have the option to be observed four times, down from six last year, with each visit lasting as little as 15 minutes — an option similar to what’s being offered to “highly effective” teachers this year. The agreement means that many administrators will be required to spend less time in classrooms.

“It gives the principal the choice to limit paperwork, and free up more time to work with teachers who are struggling and less time with effective teachers,” said United Federation of Teachers President Michael Mulgrew, who formally agreed to the deal on Tuesday.

It’s unclear how many teachers will now have the choice to reduce the number of observations because officials have not yet said how many city teachers received “effective” and “highly effective” ratings last year. But if the city follows statewide trends, the number could be significant. In the 2012-13 school year, 94 percent of teachers statewide, excluding New York City, received one of the top two ratings.

The change is the latest in a series of tweaks to the city’s new teacher evaluation system, which debuted last year. It also represents another way evaluations have evolved from what State Education Commissioner John King imposed, nearly two years ago, into the city’s vision.

The system that King created, after the city and teachers union could not agree on one on their own, increased the number of required classroom observations across the board. The system offered teachers the option to have six unannounced, shorter observations or three informal observations and one formal, full-class-period observation. Both the city and teachers union had asked King to require fewer required observations.

But at schools where many teachers opted to receive the six observations, many principals complained that they were being made to spend as much time with top-performing teachers as with the struggling ones.

“Workload is one of the most important issues for our members as it is for teachers,” said CSA President Ernest Logan said.

The new UFT contract already created a new option allowing “highly effective” teachers to be observed in three short observations. The CSA pushed for a similar reduction for “effective” teachers, and first announced to its members that a deal was in place last week. A final deal couldn’t be inked without the teachers union, which formally signed off on Tuesday, a UFT spokeswoman said.

The deal comes after the school year has begun, and the next step for schools is giving teachers their new choices—presenting challenges for some schools that have already begun to plan teacher observations. CSA officials, who are still fighting the de Blasio administration over retroactive pay for some of its members, expressed frustration that the Department of Education didn’t immediately notify schools since the change have implications for early-year planning.

“We have stressed how important this is that the DOE get this out,” said CSA Vice President Mark Cannizzaro. “Hopefully that’s going to happen very soon.”

On Tuesday, some educators echoed that sentiment.

“How soon will we have full details, as many of us have completed our individual conferences?” Mitchell Poska, an assistant principal at Franklin Delano Roosevelt High School in Brooklyn, posted on CSA’s Facebook page.

A spokeswoman for the department did not immediately comment on the deal.