The financial aspects of the deal also worried some observers. Moody’s, the bond-rating agency, said the contract resolved long-standing budgetary uncertainty but that its costs would add to future deficits and its health savings could face “roadblocks.” The city comptroller discovered basic accounting problems with the deal the de Blasio administration struck, asserting that certain costs in the contract be accounted for in earlier city budget years.

The results of the vote were tabulated by the American Arbitration Association, which collected anonymous ballots that had been distributed to 106,000 unionized workers, including 80,000 teachers.

“We are going to help good educators stay and grow in this profession, and usher real reform that will lift up kids across the whole system,” the mayor said in a statement after the results were announced. “At the same time, we are securing unprecedented health care savings, which make this a fiscally responsible contract that protects our budgets and our taxpayers.”

The contract holds the workday to 6 hours and 20 minutes, and raises the starting salary to $56,709 by the end of the contract, from $45,530, the union said. It raises the top salary to $119,471 from $100,049. Teachers nominated by principals to be mentors for other teachers are eligible for bonuses of $7,500 to $20,000.

The contract allows some schools, with teachers’ consent, to adopt more flexible work rules, an attempt to mimic successful charter schools. It also replaces time set aside for tutoring struggling students with time for more teacher training and parent-teacher communication, a change the administration says will improve student and teacher performance over all. It will also give the Department of Education more authority to fire some of the 1,200 teachers who draw full salaries but have no permanent positions, from the so-called absent teacher reserve, the bulk of whom are casualties of the Bloomberg era’s moves to close and reorganize schools.

“The new agreement gives teachers and parents a larger voice in how their schools are run, and how they can better serve their students,” Mr. Mulgrew said in a statement Tuesday. “We now have to work together — teachers, parents and the D.O.E. — to make these innovations successful.”

In its review of the contract, Educators 4 Excellence, an advocacy group of teachers that often was aligned with the Bloomberg administration’s goals, gave the contract a barely passing grade and said it “overlooked several critical issues,” such as class sizes and a tenure-granting process that the group believes ought to be more closely linked to teacher performance. Still, the review said, the contract “leaves room for optimism,” for a work force thirsty for a new deal.