Cuomo, a Democrat, had championed the proposal and had lobbied the Legislature to approve it.
"This law strikes the right balance between a teacher's right to privacy and the parents' and public's right to know," Cuomo said in a statement. "New York's children deserve a top-quality education, and the state's new teacher evaluation system will ensure that teachers and principals are held responsible for student performance."
When the Legislature approved the bill last week, teachers' unions called it a "tremendous victory."
Earlier this year, a state judge, in a case involving New York City teachers, ruled that evaluations should be publicly available. Lawmakers who supported limiting access said they wanted to protect teacher privacy and avoid "media exploitation."
School districts across New York are still hashing out details of what will go into teacher assessments. According to union officials, about 65 districts already have reached agreements.
Districts can begin submitting agreements July 1 and have until Feb. 1 to complete them -- or risk their share of a statewide 4 percent increase in school aid. Cuomo administration officials said Monday the earliest that the evaluations would likely be available will be fall 2013.