The vote Thursday came despite a request by Gov.-elect Robert Bentley to delay any vote until newly elected board members are seated.
Bentley, who will become president of the board next year, says the standards should be determined by local school boards and parents, not the federal government.
Gov. Bob Riley joined the majority in approving the national standards.
State school officials say they were developed by the National Governors Association and the Council of Chief State School Officers.
They say the standards will make it better for children who move from one school system to another.