He obtained a doctorate in pastoral theology from Rome-based Pontifical Lateran University.
In January 2008, the Cardinal-designate was appointed the Local Ordinary of Kigoma Diocese in his native country of Tanzania, and Consecrated Bishop some three months later.
He was appointed Adjunct Secretary of the Congregation for the Evangelization of Peoples (Propaganda Fide) and president of the Pontifical Mission Societies (PMS) with the personal title of Archbishop in June 2012.
In 2017, Archbishop Rugambwa was appointed Secretary of Propaganda Fide, the Vatican department tasked with “the transmission and dissemination of the faith throughout the whole world” that has “the specific responsibility of coordinating and guiding all the Church's diverse missionary efforts and initiatives”, where he served until March 2023.
During his service at the Vatican, the Tanzanian Cardinal-designate defended the youth facing migration challenges.
In a July 2022 report, Archbishop Rugambwa urged members of the Association of the Regional Episcopal Conferences of Central Africa (ACERAC) at their Plenary Assembly in Mongomo, Equatorial Guinea, to defend the youth as they are vulnerable to migration challenges.
“The Episcopate of Central Africa should be the mouthpiece and tireless defender of youth in their respective governments and societies, drawing attention to the reality of the migratory phenomenon, which sees young people at the forefront, especially as victims,” he said during the assembly that sought to address the “Phenomenon of the Youth Migration: The case of Central Africa.”
In August 2019, the Cardinal-designate hailed the establishment of ACI Africa as being in line with the desires and goals of the Vatican-based Congregation responsible for missionary work across the globe.
“We are indeed as a congregation very privileged because evangelization through media for us is also one of our priorities,” Archbishop Rugambwa said in his goodwill message ahead of the ACI Africa launch in August 2019.
Other Cardinals from Africa that Pope Francis named on July 9 include Archbishop Stephen Ameyu Martin of Juba in South Sudan, and Archbishop Stephen Brislin of Cape Town in South Africa.