Family, friends and former colleagues at the mass in the Sacred Heart Church, Donnybrook, Dublin, heard Mr Costello had been a great legal mind in modern Ireland.
Chief mourners at the mass were Mr Costello’s wife, Joan, and his children John, Joan, Caroline and David. The 84 year-old died after a long illness.
Mr Costello served as Attorney General from 1973 until 1977 and his appointment to the High Court. His career on the bench spanned 20 years, culminating in his appointment as President of the High Court.
His legacy includes the establishment of the office of the Director of Public Prosecutions to safeguard the independent prosecution of crime.
In his homily, Monsignor Richard Sherry said: “Declan Costello was a great Christian who walked among us and offered us a new vision of Ireland.”
Monsignor Sherry said the former TD had lived in the shadow of death for a long time before he passed away. Mr Costello had been a great family man and a private person, mourners were told, who had also enjoyed greatly the company of his grandchildren.
The clergyman said the former politician had a great understanding of life.
“Another of Declan’s greatest gifts was what I call the way he could use his profound awareness, as he experienced the soul of 20th century Ireland.
“Declan tried to translate his awareness… into concrete ideas for a better Ireland. He was a prophetic voice.”
Taoiseach Enda Kenny and Chief Justice John Murray were among the mourners.
They were joined by members of the judiciary, politicians and legal chiefs.
Mr Costello was laid to rest in Deansgrange cemetery.