The deal was endorsed Wednesday night by the union's 3,400-member delegate assembly.
The contract gives teachers back pay worth the equivalent of nearly 8 percent of their salaries.
The ratification vote will be done by secret mail ballots that should be counted by early June.
Negotiators reached a deal May 1 after a nearly five-year labor dispute.
But some union members aren't happy with the contract. The Movement of Rank and File Educators says proposed raises match the inflation rate and don't address disparities in class size and learning conditions between city schools and suburban districts.
The 9-year agreement will implement a number of groundbreaking reforms that the city says will make schools laboratories of innovation and improve public education for every student, while also making important changes that will provide more than $1 billion in health care cost savings over the next four years.