Hundreds of mourners from politics, business, horse racing and music gathered at the Church of the Sacred Heart, in Dublin to pay their last respects.
Pope Francis sent a telegram honouring Mr Reynolds' work towards peace and reconciliation in Northern Ireland.
"Recalling with gratitude the late taoiseach's efforts to promote peace and reconciliation in Ireland, His Holiness prays for the eternal repose of his soul," the pontiff said.
Mr Reynolds, who had been suffering from Alzheimer's died aged 81 last week.
He is survived by his wife Kathleen, two sons and five daughter. The family took centre stage at the state funeral where Irish Prime Minister Enda Kenny and President Michael D Higgins joined former prime ministers Liam Cosgrave, John Bruton, Bertie Ahern and Brian Cowen.
Philip Reynolds, his eldest son, described his father as "an innately good man" who has "slipped away to do his next deal".
He touched on suggestions that Mr Reynolds' legacy of helping to create lasting peace in Ireland was only celebrated with his death and not while he was alive.
"Few of us will ever bend the course of history but our collective efforts can make this a better place. How successful he was in his life is for others to judge. To us it does not matter, he was simply brilliant," he said.
"To know dad was to understand him - satisfied with his life's work, because he lived it with goodness at its core, a generosity of spirit that people liked and a brilliance of mind to bring those two fantastic attributes together to make a difference."
The coffin was draped in the country's tricolour and pall bearers from the Defence Forces carrying Mr Reynolds' remains from the church and again at Shanganagh Cemetery in Shankill.