Bishop Daly made headlines worldwide when he raised a blood-soaked handkerchief and guided the body of a dying teenager through army gunfire on Bloody Sunday.
He died on Monday after a long illness and his funeral Mass was held at St Eugene's Cathedral in Derry.
Large crowds turned out from across Ireland and beyond to attend the service, at which Dr Daly's sisters Marion and Anne, nieces and nephews were among the chief mourners.
In a piece read out at Mass, Pope Francis said he was "saddened" by Dr Daly's death.
"[The pope] sends heartfelt condolences to his family and to the clergy, religious and lay faithful of the Diocese.
"Recalling Bishop Daly's generous and dedicated episcopal ministry in the service of peace and justice, His Holiness joins you in prayerful thanksgiving for his life and in commending his soul to the merciful love of God Our Father.
"To all who mourn the late Bishop's passing, Pope Francis cordially imparts his Apostolic Blessing as a pledge of hope and consolation in our Lord Jesus Christ."
Bishop Daly was buried in the cathedral grounds after Mass.
In later life the retired bishop was reluctant to discuss the moment that arguably best symbolised his Christian ministry; in death it has largely defined him.
As a young priest he famously waved the bloodied rag as he led a brave group bearing fatally injured civil rights protester Jackie Duddy, 17, to safety in Londonderry in Northern Ireland on Bloody Sunday.
Paratroopers had opened fire and killed 13 people. Fourteen were injured and another was to die later.
Bloody Sunday has been described as one of the catalysts of IRA recruitment and the 30-year conflict which left more than 3,000 dead and many others injured.
In his homily, Bishop Donal McKeown of Derry said: "Today, we come to hand back to God one who was grateful for how he had been blessed in life - and one whose ministry has been an instrument of God's peace for so many people.
"Edward Kevin Daly, your time of faithful service is over. You have fought the good fight, you have run the race, you have kept the faith (Cf. 2 Tim 4:7).
"As you breathed your last and commended your spirit into God's hands, you could pray the words of Simeon in the Gospel 'Now let your servant go in peace according to your promise'."
