The evaluation system that State Education Commissioner John King imposed on New York City today fulfills requests made by both the Bloomberg administration and the United Federation of Teachers.

In a unique move, it also delegates crucial decisions about how teachers will be rated to the city’s roughly 1,600 non-charter public schools and, in some cases, to teachers themselves.

Gov. Andrew Cuomo asked lawmakers to allow King to impose an evaluation system after city and union officials failed to agree on one by a January deadline. Starting from broad parameters set out in state law, each side made its case in position papers and in-person presentations last month, and King issued his final determination tonight.

“Following years of delay, today we can finally say that every school district in the state of New York has a teacher evaluation system in place based on some of the most stringent and comprehensive standards in the nation,” Cuomo said in a statement. “The mayor didn’t win and the union didn’t win. Today, the students won. Finally.”

King said the plan would remain in effect through the 2016-2017 school year — or unless the city and teachers union negotiate a different plan that follows the state’s evaluation law. That could happen as soon as next year, when a new mayor takes office and must negotiate a contract with the teachers union.

“If we feel it’s not going well, we will advocate for changes next year,” said UFT President Michael Mulgrew.

Under the plan, which King has not yet published in full, teachers will get to decide how frequently they want to be observed and whether they will let administrators judge their teaching by videotape. Teachers will be able to choose whether administrators see one full period of instruction along and two shorter snippets, or whether administrators come six or more times for short visits. Both options require more observations than either the city or UFT asked for, and both represent substantial change from the old system, under which most teachers were assessed on the basis of a single announced observation.

And teams of educators at each school, chosen jointly by the UFT and the principal, will get to choose the assessments that will generate the 20 percent of teachers’ ratings that must be based on locally selected measures of student growth. (King picked a default in case they can’t decide, or the principal doesn’t like their choice.) Some schools might administer additional pencil-and-paper tests, while others might ask teachers to administer performance assessments that are embedded in their daily instruction.

The flexibility, which both city and UFT officials wanted, recognizes the diversity of schools in New York City, King said.

On other significant issues, King sided more clearly with one party or the other. Principals will have to consider all of the elements of the Danielson Framework for observing teachers, not just some, as the Department of Education had wanted. UFT President Michael Mulgrew said he worried the city would ask principals to focus only on the hardest components while ignoring others that are important, such as lesson planning. King said he would also require principals to document each of their observations in writing, which the union wanted but the city said would create unnecessary paperwork.

“I wanted a plan I thought was fair and more importantly followed the spirit of the law, and I think we have the beginning of that,” Mulgrew said.

But King also carved out a small role for student surveys, which union officials had sworn they would never accept. Starting in the 2014-2015 school year, student surveys will count for 5 percent of the ratings of teachers in third grade and beyond. And King’s final plan did not reflect issues that the union raised if they were not required under the state’s evaluation law, such as for all teachers to have curriculum given to them before they could be evaluated under a new system.

Department of Education officials said they had gotten almost everything they asked for and in fact ended up with a system they liked more than what they almost agreed to in January. Chancellor Dennis Walcott said he considered King’s plan “a major victory for students and staff.”

In January and last year, Mayor Bloomberg rejected teacher evaluation deals because he said the systems that would go into place would not result in any teachers being fired.

King pushed back against that outlook today, in the first paragraph of his press release touting the new evaluation system.

“There are strong measures to help remove ineffective teachers and principals, but let’s be clear: New York is not going to fire its way to academic success,” King said.

City and union officials’ next task is to figure out how to implement the new system. City officials said part of the $100 million in teacher training funds it has set aside for this year will go toward preparing educators for the new evaluations. One required component for teachers whose students do not take state tests, “Student Learning Objectives,” will be completely new to almost all city educators but count for 20 percent of their scores.

Mulgrew said the rollout of the new system would be crucial to determining whether it helps teachers improve, as the union hopes will happen, or amplifies mistrust between teachers and the Department of Education.

“None of this is going to be good if the implementation starts out horrendously,” he said.

King also announced a system for evaluating principals. The union that represents principals, the Council on School Supervisors and Administrators, actually reached an agreement with the Department of Education, with “the strong intervention of Commissioner King,” according to President Ernest Logan. That evaluation system hews closely to how principals have been rated in the past but increases the role of superintendent observations and introduces an appeals process for principals who get low scores.