The church is the national church for the Ukrainians in Rome, a meeting place and religious center for the community. The Divine Liturgy is celebrated according to the Byzantine-Ukrainian rite, whilst still in full communion with the Catholic Church.
The church was built in 1967-1968 on the orders of Cardinal Josyf Slipyj, the Major Archibishop of Lviv who had spent about 18 years in a Soviet gulag, and subsequently released but not allowed to return to the Ukraine.
It is modeled after Kiev's own Saint Sophia Cathedral. The relics of Pope Clement I (88-97) are kept in the church. Following the Byzantine rite, the church has an iconostasis, painted by Juvenalij Josyf Mokryckyj.
In 1998 the church was raised to the status of a minor basilica.
The first Cardinal-Priest of Santa Sofia was Myroslav Cardinal Lubachivsky. Lubomyr Cardinal Husar, MSU, Major Archbishop of Kyiv-Halych, held the titular church from his appointment as a cardinal on 21 February 2001 until his death in 2017.