The 89-year-old died peacefully at around 2pm, in a nursing home in Co Clare.
The controversial bishop left Ireland in 1992 after it was discovered that he had fathered a son.
He spent 14 years in exile in South America but returned to Ireland, and has spent the last number of years in a nursing home.
He had been suffering from dementia and was unwell in recent years.
Funeral details have yet to be announced.
In a statement tonight the family of Bishop Casey have described him as a "great source of love".
“On behalf of his son, Peter, his brother, Father Micheál, his sister, Ita Furlong, nieces and nephews, grand-nieces and grand-nephews, great-grand nieces and great-grand nephews, we wish to acknowledge the priestly work of Bishop Eamonn, especially in the pursuit of social justice for the marginalised, as evidenced by his work with Shelter in London in the 1950’s and 1960’s and later with his involvement in the setting up and development of Trócaire," the statement said.
"Notwithstanding the demands on his time, Bishop Eamonn was a great source of love and support, making himself available to celebrate and to empathise with us in all our important family occasions."
“We wish to thank all of those who supported him in the past, in particular, the clergy and the people of the dioceses of Galway and Kerry, the Irish community in London, his many friends in Limerick and throughout the country and abroad.
Deputy Pat Casey, who is a nephew of the late former Bishop also paid tribute.
"Our family loved Eamonn, 'uncle Eamonn' as he was known to many, was as jovial and as caring a man to his family, as he was to the many people he served in his public ministry as a priest and bishop," he said in a statement to Independent.ie
"Eamonn Casey was a man whose heart belonged to the West of Ireland. Born in Kerry, raised in Limerick, Uncle Eamon was devoted to his Catholic ministry and to the people of his parishes and subsequently his dioceses.
"Uncle Eamonn worked hard in trying to achieve social justice for many causes close to his Christian belief such as the plight of Irish emigrants, the courage of the Dunnes workers protest against apartheid South Africa and the people of San Salvador who suffered brutal oppression from their Government.
"As a family we are also acutely aware of the controversies in Uncle Eamonn’s life. He has passed from this life during the Christian season of Lent which considers such themes as sacrifice, atonement and reconciliation," he added.
He also thanked the staff at Carrigoran nursing home in Clare where he passed away.
Trocáire have also paid tribute to the late Bishop and their former chiarman.
He was appointed chairman shortly following the organisation's inception in 1973 and "shone a spotlight on situations of injustice overseas" the charity said.
Archbishop Eamon Martin has also joined those paying their respects to Bishop Casey, praising his work overseas.
Canon Muchael McLoughlin, of the Diocese of Galway, Kilmacduagh and Kilfenora has remembered Bishop Casey as someone with "boundless energy" who had the ability to uplift people.
"Bishop Eamonn brought blessings to many people. But to be human is to be both blessed and to be flawed. Some of his actions caused great hurt and the circumstances giving rise to his resignation in 1992 have been the subject of ongoing analysis. Bishop Eamonn asked for forgiveness from all those that he hurt and he went on to minister in both Ecuador and England before returning to Ireland to retire in January 2006," he said.
The Bishop, who was both high-profile and a popular media personality in the 70s and 80s, was at the centre of one of the first major scandals to hit the Catholic Church in Ireland.
In 1992 it emerged that he had engaged in a love affair with Annie Murphy, and had fathered a child with her.
The news scandalised Catholic Ireland, forcing him to leave in a storm of controversy.
It also emerged that the Bishop, who was already a household name and had introduced Pope John Paul II at Ballybrit Racecourse in Galway in 1979, had been making payments to Ms Murphy for 18 years. To do so he sometimes used money from diocesan funds.
Ms Murphy negotiated a $150,000 settlement from the Bishop in 1990 and went on to secure a book deal: 'Forbidden Fruit: The True Story of My Secret Love for the Bishop of Galway'.
Annie was a second cousin once removed from Bishop Casey and the pair had met once when Annie was young but began their affair in 1973, meeting up all over Dublin, after she moved here.
"When Eamonn picked me up from the airport that day in 1973, a light went on, there was a spark, that was it. It was as if you believe in reincarnation and we had just picked up from a previous life, as if I had known him all my life," she said in 2012.
"I had never known anything like that or known anyone like Eamonn. He was electric, he drove like a lunatic but I didn't feel unsafe, although I gave him a very hard time over it."
Bishop Casey urged her to give the child up for adoption when they learned of her pregnancy.
Reflecting on that as a woman in her 60s, Ms Murphy said Bishop Casey had no regrets about joining the priesthood.
"The Church was his cornerstone. He loved people and helping people and he had no regrets about being in the priesthood, but, all the same, he wanted it," she said.
"I never met anyone so stubborn in all my life. Eamonn did a lot of good, but he was incredibly stubborn -- he wouldn't meet you half way. He was able to separate parts of his life, his indoctrination as a priest was strong."
After the new broke Bishop Casey was forced to live in exile in Central America before eventually returning to Ireland in 2006.
In a televised statement that year, his first public statement in 14 years, he apologised for the hurt he caused in the past.
Speaking from his Co Galway home, he had appealed for prvacy in his retirement.
"I regret that in the past I let a number of people down. It caused great hurt to some and for that I am deeply regretful and sad," he said at the time.
His son Peter Murphy, who is based in Boston, developed a relationship with Bishop Casey over the years and visited him in Ireland in 2013.
He has said in the past that he planned not to attend his dad's funeral but would find his own way to grieve and pay his respects.
Peter has said he was "proud" of his dad and criticised the Catholic Church's treatment of him stating "treated paedophiles better than they treated my dad".