Ssemogerere was born on 30 June 1956 at Kisubi, in present-day Wakiso District in the Buganda Region of Uganda. This location is in the Roman Catholic Archdiocese of Kampala.
He attended Kigero Primary School before transferring to Kisubi Boys Primary School. He then studied at St. Maria Goretti Senior Secondary School Katende, where he completed his O-Level studies. In 1976, Ssemogerere and seven other young men became pioneer students at St Mbaaga Seminary at Ggaba. This was the first class of this seminary, which specializes in admitting men to train as priests when they are older than usual, and without attending minor seminary.
In 1978, the late Cardinal Emmanuel Kiwanuka Nsubuga sent Ssemogerere to the Saint Francis de Sales Seminary, in Milwaukee, Wisconsin, in the United States, where he graduated with a Master of Divinity degree in 1982. On 21 November 1981, he was ordained a deacon by Archbishop Rembert George Weakland, the Archbishop of the Roman Catholic Archdiocese of Milwaukee.
He was ordained a priest on 3 June 1983 at Kampala, by Cardinal Emmanuel Nsubuga, Archbishop of Kampala. He served as a priest in the Roman Catholic Archdiocese of Kampala, until 4 June 2008.
He was appointed bishop of the Roman Catholic Diocese of Kasana-Luweero, on 4 June 2008. He was consecrated as bishop on 23 August 2008 at Kasana-Luweero by Archbishop Cyprian Kizito Lwanga, Archbishop of Kampala, assisted by Cardinal Emmanuel Wamala, Cardinal-Priest of Sant’Ugo, and Cardinal Emeritus of Kampala and Archbishop Paul Tschang In-Nam, Titular Archbishop of Amantia and Papal Nuncio to Uganda at that time. On Thursday the 8th April he was appointed Apostolic Administrator of Kampala archdiocese by Pope Francis after the sudden death of Dr. Cyprian Kizito Lwanga whos the Archbishop of Kampala.