Educated up to school certificate at Tamale Government Secondary School. He then joined the army in 1960 and after early officer cadet training in Ghana went to Sandhurst, returning to a regular commission in 1963.
He was commissioned as a lieutenant in the Ghana army in 1963. He rose through the ranks after attending courses in Ghana and the United Kingdom.
Colonel Roger Felli was one of six senior military officers who had previously served in government, executed by firing squad at the Teshie Military Range at Teshie, at the outskirts of Accra.The executions were ordered by the AFRC and carried out on June 26, 1979. The other officers executed with him were two former heads of state of Ghana, Gen Fred Akuffo and Lt Gen Akwasi Afrifa and three other military officers, namely Air Vice Marshal Boakye, Maj. Gen R.E.A. Kotei and Rear Admiral Joy Amedume. They were buried in unmarked graves at Adoagyiri near Nsawam in the Eastern Region of Ghana.
He did a number of further training courses in Britain, specialising in Signals. This equipped him for his appointment as adjutant of the No. 1 Signals Regiment and later Director of Communications at the Communiations Directorate. He was acting commander of No. 1 Signal Regiment at the time of the Ghana coup, when he was given his first major civilian appointment as Commissioner for Works and Housing and was made a member of the National Redemption Council.
After the overthrow of Dr. Kofi Abrefa Busia's Progress Party government on January 13, 1972, the then Major Felli became a member of the ruling National Redemption Council led by General (then Colonel) Ignatius Kutu Acheampong. He was appointed the Commissioner for the Works and Housing Ministry in the new government. He later also held the portfolios of the Trade and Industry Ministry and the Finance and Economic Planning Ministry respectively. Colonel (then Major) Roger Felli was appointed Minister of Foreign Affairs in 1975. He held this position till the coup d'état of June 4, 1979 which brought the Armed Forces Revolutionary Council (AFRC) led by Flt. Lt. Jerry Rawlings to power.