When territory is annexed to any city pursuant to section 81.200, the common council shall, by ordinance, organize the same into a new ward or wards, or attach the same to some existing ward or wards long enough before the next ensuing municipal election to enable voters in such annexed territory to register, and all other proper steps to be taken according to law, so that the voters of such annexed territory may have full opportunity to register and vote at such election. Actual residents of any territory at the time of annexation thereof to any city as provided in section 81.200 shall, if otherwise qualified, be voters of the city, and be eligible to any office therein at the next municipal election following such annexation. In case of redistricting or division of the city into wards, creation of any new ward or wards, or change of boundary in any ward or wards, every voter residing in any ward at any municipal election next thereafter, duly registered, shall be a voter of such ward, and nothing in this chapter contained shall be so construed as to prevent any voter from voting or being eligible to any office by reason merely of such redistricting or division or creation of any new ward or wards, or change in the boundary of any ward or wards.