Rev Séamus Hegarty passed away after an illness in Letterkenny University Hospital, Co Donegal.
He served this diocese from 1994 -2011 and retired after announcing he was diagnosed with a condition which was "irreversible and progressive".
Prior to that, Rev Hegarty was ordained Bishop of Raphoe in 1982.
Church leaders in Ireland have been paying tribute to him.
Archbishop Eamon Martin honoured Rev Hegarty as a leader who passionate about his advocacy on education and emigrants.
"Bishop Hegarty often intervened at conference meetings to draw attention to the personal, social and economic challenges facing emigrants, and he supported efforts to raise vital funds for the mission to those who face challenges far from home," he said.
During the Irish Catholic Bishops' Conference, Archbishop Eamon also reflected on his personal relationship with Rev Hegarty.
"I am grateful to Bishop Séamus for his encouragement and support to me as my bishop in Derry from 1994 until his retirement in 2011. He was unstinting in his support for my role as teacher and President of Saint Columb's College.
"Having been a school principal himself for many years, he was passionate about the importance of education for young people and he had a strong awareness of the issues facing school staff and managers.
"He worked tirelessly to secure the new school sites for girls' post-primary education in the City of Derry and to ensure that the very best facilities were being made available for our young people."
Most Rev Donal McKeown, Bishop of Derry said: "Even though Bishop Séamus Hegarty had been in declining health for a number of years, it was with sadness that I heard about his death.
"Bishop Séamus had an impressive dedication to his role as a priest and bishop, with a special expertise in education. His concern for Irish emigrants around the world was constant and heartfelt."
Most Rev Alan McGuckian SJ, Bishop of Raphoe, has also offered his condolences.
He said Hegarty's ministry as bishop was deeply challenged because of serious crimes of child sexual abuse perpetrated by priests in his diocese.
He was confronted about his management of the situation and admitted to his failures.
Following his resignation in 2011, Rev Hegarty asked for forgiveness from those who suffered cruelly and said: "I am deeply sorry that anyone was hurt through my management of allegations historically."
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