The full-day strike action replaces previously planned three-hour strikes.
"We had a clear message from members at the paid union meetings and from feedback and surveys.
"It is 24 years since educators have gone on strike and this is not an action we are taking lightly," she said.
The statement quoted lead teacher negotiator Liam Rutherford as saying public opinion polling showed strong support for more taxpayer dollars being spent on education, including a significant pay increase for educators.
"The National Party's U-turn on teacher pay and new desire for smaller class sizes means there is now no political opposition to addressing the crisis in education," he said.
"The members' decision to take industrial action shows the degree of frustration and conviction among teachers and principals."
Green said it was crucial to attract and retain great teachers.
"Teachers and principals need to have time to teach, time to lead, and be valued for the professionals that we are. And all children need to get the support they need to thrive at school," she said.
The online ballot was run by an independent company Electionz.com.
NZEI and the Ministry of Education agreed yesterday to enter mediation over collective agreement negotiations.
Any outcome of the mediation will be taken back to NZEI members for their consideration.