The act came after the Senate fell one vote shy of overriding the governor's veto of a similar plan Republicans inserted in the state budget.
The Assembly voted 62 to 31 for the legislation.
The plan approved Wednesday is similar to the provision Doyle vetoed from the budget.
It makes minor changes to address Democratic complaints that the limits would hurt economic development.
That includes a provision to ensure the limits don't apply to tax incremental finance districts, a tool local governments use to spur economic growth.
Republican Assembly Speaker John Gard says lawmakers will try again if this bill doesn't become law.
Democratic Representative Tom Hebl says Republicans are just trying to generate a roll call vote to use against Democrats in next year's elections.