In 1949 Velyki revived and expanded Analecta Ordinis S. Basilii Magni. He published a number of important documentary collections:
- Actae S. Congregationis de Propaganda Fide, 1622–1862 (5 vols, 1953–5),
- Documenta Pontificum Romanorum Historiam Ucrainae Illustrantia, 1075–1953 (2 vols, 1953–4),
- Litterae S. Congregationis de Propaganda Fide, 1622–1862 (7 vols, 1954–7),
- Epistolae Metropolitarum Kioviensium Catholicorum, 1613–1839 (9 vols, 1956–80),
- Litterae Nuntiorum Apostolicorum, 1550–1900 (14 vols, 1959–77),
- Documenta Unionis Berestensis eiusque Auctorum, 1590–1600 (1970),
- Litterae Episcoporum, 1600–1900 (5 vols, 1972–81),
- Litterae Basilianorum, 1601–1760 (2 vols, 1979).
He established the series Ukrainska dukhovna biblioteka (The Ukrainian Spiritual Library), which published over 70 titles, 17 of which he wrote. His book on religious persecution in Ukraine, Bila knyha (The White Book, 1952), was translated into German, English, and Spanish. He also wrote a history of the Sisters Servants of Mary Immaculate (1968), Svitla i tini (Lights and Shadows, 1969), Ukraïns'ke khrystyianstvo (Ukrainian Christianity, 1969), and Z litopysu khrystyians'koï Ukraïny (From the Chronicle of Christian Ukraine, 9 vols, 1968–77). He contributed many entries to Entsyklopediia ukraïnoznavstva and Encyclopedia of Ukraine and drafted the missive from the Ukrainian Catholic church hierarchy on the anniversary of Saint Olha and the official statement issued by the Ukrainian bishops regarding the release from Siberia of Metropolitan Josyf Slipyj.