The cathedral's name comes from the Hagia Sophia cathedral in Constantinople. The first foundations were laid in 1037 by prince Yaroslav I the Wise. The exterior was covered with plinths. Dimensions: 37×55 meters. The cathedral has 5 naves, 5 apses, and (quite surprisingly for a Byzantine structure) 13 cupolas (domes). It is surrounded by two-tier galleries from three sides.
In 1934 the structure was confiscated by the Soviets and designated an architectural and historical museum/reserve, including the surrounding architectural ensemble of the 17th–18th century. The cathedral was the first Ukrainian patrimony to be inscribed in the World Heritage List.