Schools will have six months to put anti-bullying policies into place once Gov. Rick Snyder signs the measures into law.
A spokeswoman says the governor plans to do that Tuesday afternoon.
Michigan recently ended up in the national spotlight after GOP senators passed an anti-bullying bill that included a clause saying the legislation didn't "prohibit a statement of a sincerely held religious belief or moral conviction."
Democrats say the exceptions would have made it even easier to bully.
The House and Senate last week passed a version without that language.
Michigan is one of only a few states without a law requiring anti-bullying policies in schools. Efforts to pass a law fizzled for years until Snyder this spring urged lawmakers to get an anti-bullying law on the books.