The first election to the City and County of Swansea Council was held on 4 May 1995. It was followed by the 1999 election. On the same day there were elections to the other 21 local authorities in Wales and community councils in Wales.
All council seats were up for election. These were the first elections held following local government reorganisation and the abolition of West Glamorgan County Council. The ward boundaries for the new authority were based on the previous Lliw Valley Borough Council and Swansea City Council although the number of members elected for individual wards was reduced. Conservative candidates were heavily defeated.
Most sitting members of West Glamorgan County council sought election to the new authority. A number were also members of the previous district councils but others contested a ward against a sitting district councillor.