Joseph Kiwanuka was born in Nakirebe, Mpigi District, to Catholic parents, Victoro Katumba Munduekanika and Felicitas Nankya Ssabawebwa Namukasa.

Streicher then sent the young priest to Rome to study canon law, in an attempt to prevent him from entering the White Fathers' novitiate, which had invited Kiwánuka in July of that year.

In Rome, Kiwánuka studied at the Pontifical University of St. Thomas Aquinas, Angelicum, from where he later obtained his doctorate in canon law, with a dissertation on marriage.

On May 25, 1939, a day before the tenth anniversary of his priestly ordination, Kiwánuka was appointed the first Apostolic Vicar of Masaka and Titular Bishop of Thibica by Pope Pius XII.

He received his episcopal consecration on the following October 29 from Pope Pius himself, with Archbishops Celso Costantini and Henri Streicher, MAfr, serving as co-consecrators, in St. Peter's Basilica.

His last great act was issuing a pastoral letter on political leadership and democratic maturity during the governmental crisis of President Milton Obote.