After a city or village has made provisions for financing its proportionate share of the costs and has complied with the provisions of sections 18-617 to 18-636, and the provisions of section 18-633 have been complied with, such city or village shall proceed to construct, in accordance with plans and specifications previously approved, the viaduct or subway, or such city or village is hereby authorized to contract for such construction in accordance with such plans and specifications. Any such contract shall be awarded as provided by law.