Dr Morgan is the longest serving archbishop in the worldwide Anglican Communion after having spent 24 years as a bishop.
He will retire on his 70th birthday at the end of January, just months after the death of his wife from cancer.
"It has been an enormous privilege to serve as Archbishop of Wales and Bishop of Llandaff and to do so during such a momentous era in Welsh life," he said.
"It's been a rollercoaster ride but all along I have been sustained and inspired by the people I meet, day in day out, who live out God's love in every part of Wales through their commitment and devotion to their churches and communities.
"I would like to thank all those who have supported, shared and upheld me in my ministry over the years, particularly since Hilary's death - the loss of her love, encouragement and friendship has been enormously hard to bear.
"Over the years I have seen Wales grow in self-confidence as a nation and I now have every hope that this will be nurtured and enriched with the continued support of the Church in Wales."
The Archbishop of Canterbury Justin Welby said he was an "extraordinary servant" who would be "deeply missed".
The First Minister of Wales Carwyn Jones praised his "vast contribution" to Welsh life.
During his tenure as Archbishop, Dr Morgan has overseen a change in Church law to enable women to be ordained as bishops and the implementation of a radical strategy, 2020 Vision, to help the church grow and prosper in the approach to its centenary year.
Originally from the small mining village of Gwaun-Cae-Gurwen in the Swansea valley, Dr Morgan was elected as the 12th Archbishop of Wales in 2003, following Dr Rowan Williams after his appointment as Archbishop of Canterbury.