Dr Hegarty died at Letterkenny University Hospital on Friday at the age of 79 following a long illness.
A native of Kilcar in Co Donegal, he served as Bishop of Raphoe from 1982 until he was appointed to succeed Edward Daly in Derry in 1994.
He resigned as Bishop of Derry due to illness in 2011.
While praised for his role in the peace process, the Church leader was criticised for his handling of the clerical sex abuse scandal during his ministry as bishop.
Following his resignation, he apologised for what he described as “failures” on his part.
“I am deeply sorry that anyone was hurt through my management of allegations historically,” he said.
Paying tribute to Bishop Hegarty, Archbishop Eamon Martin said he was dedicated to education and to the plight of Irish emigrants and their families as well as Irish prisoners overseas.
“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.”
The leader of the Irish Church also paid a personal tribute to Dr Hegarty, who had been his own bishop.
“He was unstinting in his support for my role as a teacher and president of St 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.”
Archbishop Martin said Bishop Hegarty also worked tirelessly to secure new sites for girls’ post-primary schools in Derry and to ensure the very best facilities were made available to the young people of the diocese.
He added: “Bishop Hegarty was strongly pro-life and he was always anxious as a faith leader to nurture the fledgling peace process.”
“The diocese of Raphoe offers sincere sympathies to all those who loved Bishop Hegarty and grieve his passing,” he said.
Tribute was also paid by current Bishop of Derry Donal McKeown who said Dr Hegarty had an “impressive” dedication to his role as priest and bishop.
“His concern for Irish emigrants around the world was constant and heartfelt,” Bishop McKeown said.
Sinn Féin Foyle MP Elisha McCallion said many people across Derry and Donegal would be saddened by news of Bishop Hegarty’s death.
The late bishop’s Requiem Mass will take place at noon at St Eugene’s Cathedral today, after which he will be buried in the grounds.
Tags: