The cathedral is the seat for the Ukrainian Catholic Eparchy of Saint Josaphat in Parma, which was erected in 1983 during construction of the building.

[11] Designed for 500 students,[10][1] the structure was circular and features 16 one-story classrooms clustered around a central dome.

[1] The building was finally completed in early 1969, and blessed by Archbishop Ambrose Senyshyn of the Archeparchy of Philadelphia on April 20, 1969.

Brookpark Road was named the dividing line between the mother parish and the new St. Josaphat, whose boundary extended south to Medina, Ohio.

The erection of the new parish came about due to the significant growth among Ukrainian Catholics in the area (now numbering some 450 families).

[16] In 1973,[17] Father Ulicky was appointed pastor at St. Mary Byzantine Catholic Church in Johnstown, Pennsylvania.

[18] His successor, the Very Reverend Yaroslaw Sirko, continued to plan for construction of a church,[16] but died in October 1979 after a two-year battle with cancer.

[19] The Right Reverend Michael Fedorowich, assigned to St. Josaphat in December 1979, began the process of organizing committees to plan the new church.

[16] The structure was designed by the firm of McWilliams Martyniuk Schidlowski of Kent, Ohio,[20] and built under the auspices of general contractor Chopko Construction.

[16] The 500-seat building incorporated traditional features such as onion domes on the roof and an altar set in the east wall.

It also included contemporary and "futuristic" architectural details in order to reflect the then-upcoming thousand-year anniversary of Christianity's introduction in Ukraine.

[21] Robert Mikhail Moskal was installed as the first eparch (bishop) of the diocese at the unfinished cathedral on February 29, 1984.

Eparch Robert Moskal led a procession from the chapel to the cathedral carrying the Blessed Sacrament and relics of St. Josaphat, then celebrated a pontifical divine liturgy at the new church.

[16] The consecration of St. Josaphat Cathedral was delayed until May 1, 1988, the year in which Ukrainians observed the thousand-year anniversary of Christianity in Ukraine.

[16] Cardinal Myroslav Ivan Lubachivsky, head of the Ukrainian Greek Catholic Church worldwide, led the April 29 rites consecrating the main altar, assisted by Archbishop Maxim Hermaniuk of the Archeparchy of Winnipeg, Archbishop Stephen Sulyk of the Archeparchy of Philadelphia, Exarch Michel Hrynchyshyn of the Apostolic Exarchate of France, Benelux and Switzerland, Eparch Andrew Pataki of the Ruthenian Catholic Eparchy of Parma, and others.

A procession led by Cardinal Lubachivsky, Archbishop and Papal Pro-Nuncio Pio Laghi, Bishop Anthony Pilla of the Roman Catholic Diocese of Cleveland, Bishop James William Malone of the Roman Catholic Diocese of Youngstown, and Bishop Emeritus William Michael Cosgrove of the Roman Catholic Diocese of Belleville circled the building before entering.

The shrine was the result of a seven-year design and fundraising effort by the St. Josaphat Apostleship of Prayer, a group of women congregants.

The brick shrine holds a mosaic in the likeness of the painted Ukrainian icon, which was designed by Eikona Studios of Cleveland and created in Italy.

Parishioners of St. Josaphat began raising funds about 2010 to replace the cathedral's five domes, which had deteriorated over time.

Architect Christ J. Kamages was hired to design the replacements, and Unique Services & Applications installed them.

The new domes are made of stainless steel and covered with titanium nitride, a ceramic material with a brilliant gold sheen.

[26] Media related to St. Josaphat Ukrainian Catholic Cathedral (Parma, Ohio) at Wikimedia Commons