The Assembly vote was 73-4. The Senate approved the measure 35-3 last week.
Assembly Speaker Sheila Oliver, who said she wasn't involved in the compromise brokered by Gov. Chris Christie and Senate President Steve Sweeney, called the bill "imperfect" because it doesn't include exemptions for rising special education costs or losses in state aid.
"You do not allow imperfection to get in the way of what could be a start," she said after the vote. "And that is what the Assembly Dems embraced."
A spokesman for Christie said the governor would sign the bill Tuesday.
The legislation is one of dozens of proposals the Legislature will consider this summer to rein in property tax growth. New Jerseyans pay the highest property taxes in the nation, averaging nearly $7,300 per household.
The bill allows exceptions to the cap for some costs towns and school districts can't control, like pension and health care costs.
Otherwise, only voters would be able to override the cap.
