The measure passed by a vote of 35-3.
Gov. Chris Christie and Senate President Stephen Sweeney announced the compromise over the weekend.
Assembly Speaker Sheila Oliver wasn't part of the deal. But Oliver says she won't obstruct passage once the Assembly's concerns over some details are resolved. The Assembly must still consider the plan.
The Assembly and Senate passed a 2.9 percent property tax cap bill last month. Christie refused to sign it because it allowed many exemptions.
Sweeney agreed to lower the cap and Christie said towns and schools could exempt costs they have no control over, such as pensions and health care.
