St. Paul teachers were nearly unanimous Tuesday in ratifying a new contract calling for an 8.6 percent wage-and-benefit increase over two years and new limits on class sizes, among other union goals.

More than 95 percent of those voting voted “yes,” said Mary Cathryn Ricker, president of the St. Paul Federation of Teachers.

Ratification by teachers sets the stage for school board action on March 18.

The agreement is expected to cost $33 million and runs through the 2014-15 school year.

District and union negotiators reached the tentative deal on Feb. 21 after a near-24-hour bargaining session that occurred just days before teachers were set to take a strike-authorization vote.

The agreement includes teacher salary increases of 2.43 percent in the first year and 2 percent in the second year, slightly above the average 2 percent annual increases now being negotiated elsewhere in the state. Teachers in steps 15-19 and step 20 of the district’s salary schedule also would receive an additional 1 percent increase annually, under the contract.

The average St. Paul teacher salary is $68,436 — part of a wage-and-benefit package that currently totals about $92,000.

Throughout the talks, however, union leaders played down compensation proposals in favor of other goals, including moves to shrink class sizes, strengthen parent-teacher relationships and hire more nurses, social workers, counselors and media specialists.

Ricker, noting how the union’s proposal was crafted with the help of parents and community members, said in a statement: “Together, we are reclaiming the promise of public education for all St. Paul students.”

St. Paul is the state’s second-largest district with nearly 38,000 students and about 3,200 teachers.