Updated — Members of the city’s principals union voted overwhelmingly to approve their new contract with the city, officials announced Tuesday.

Ninety-one percent of the union’s membership voted to approve the nine-year, $891 million contract, which includes long-awaited raises, retroactive pay, and new incentives to work in low-performing schools. Like the deal deal struck with the teachers union earlier this year, the contract also creates new positions that offer bonuses for assistant principals and principals who take on additional leadership responsibilities.

“The state of our union is stronger than ever before,” Ernie Logan, president of the Council of School Supervisors and Administrators, said Tuesday.

Calculations posted by the union estimate that the retroactive payments, which stretch back to 2009, will be substantial for many members. In their example, a long-serving high school principal would be eligible for $76,292, though much of that wouldn’t be paid out until 2019, 2020, and 2021.

The contract also offers retroactive pay to the roughly 2,000 CSA members who had moved into administrative positions since 2009 — payments the city insisted those members were not eligible for earlier in the negotiations. In the end, the city and the union split the $120 million cost.

The 91 percent of CSA members who voted to approve the contract is slightly lower than the 93 percent of members who voted to approve their last contract in 2007. Seventy-seven percent of teachers union members voted to approve their new contract this year.