The county boards of equalization or other like boards or agencies with final authority to fix the value of property for the purposes of taxation, in all counties of the state having a population of 140,000 or more according to the last or any subsequent federal census, shall have the power and authority, from time to time, subject to the approval of the governing body of any such county, to provide for the inventory and appraisal of all taxable property of such counties, except that subject to assessment by the Department of Revenue, as a basis for the final appraisal, valuation, and equalization of the assessments of property in such counties.