Poma was born in Villanterio, and studied at the seminary in Pavia and the Pontifical Gregorian University in Rome (from where he obtained his Doctor of Theology degree in 1934).

During his tenure as Archbishop of Bologna, he founded the second House of Charity, the Mensa della fraternità or Poor People's Refectory, the Diocesan Charitas and the Mission of the Bolognese Church in Tanzania.

[2] Pope Paul VI created him cardinal-priest of San Luca a Via Prenestina in the consistory of 28 April 1969.

From 1969 to 1979, Poma served as president of the Italian Episcopal Conference; during this capacity, he warned that Catholics who support communism separate themselves from the Church.

He continued to govern the archdiocese as its apostolic administrator until the appointment of Bishop Enrico Manfredini on the following 18 March.