Rhodri Morgan has died at the age of 77.
He served in the post for almost 10 years from 1999, before retiring from politics.
Current First Minister Carwyn Jones has described him as a "great politician" saying "Wales has lost a father figure".
Swansea Council Leader Rob Stewart says Mr Morgan will be missed.
While the Welsh Secretary, Tory Alun Cairns, called Mr Morgan a "great servant to Wales".
The Liberals Mark Williams said; "Rhodri Morgan will be remembered for leading Wales in those early years, putting Welsh politics on an even footing. In what was a difficult early period for devolution, Rhodri built a coalition to deliver on the promise of devolution.
"He will be remembered as an extremely charismatic and engaging leader, and the kind words we have heard from so many today show the enormous respect and admiration for Rhodri.
"Rhodri will be hugely missed and my thoughts are with family and friends at this difficult time."
Leader of the Welsh Conservatives, Andrew RT Davies said: "Rhodri Morgan was a giant of devolved politics in Wales who served a hugely important role in stabilising the National Assembly during its formative years.
"As First Minister, his answers in the chamber were always worthy of attention and his encyclopedic knowledge across his brief ensured he was rarely wrong-footed.
"Our first meeting was not in the political arena but came after Rhodri was forced to barricade his garden late on an autumn Sunday evening after some of my cattle had misbehaved and wandered into the Morgans' - he was undoubtedly one of life's true characters.
"And while politically we didn't see eye to eye, there is no question that he was held in high regard right across the political spectrum and he will be missed by all who knew him.
"Our thoughts and prayers are with Julie and the family and as a mark of respect the Welsh Conservatives have suspended all campaigning today."
Plaid Cymru leader, Leanne Wood said: "Rhodri Morgan was much respected across the political spectrum and led Wales with distinction during a crucial period in Welsh history.
"I extend my condolences on behalf of everyone in Plaid Cymru to his family."
Plaid AM Bethan Jenkins has also been reflecting on Mr Morgan's contribution to Welsh politics and the devolution process.
Alun Michael, Police and Crime Commissioner for South Wales was First Minister before Rhodri Morgan. He's shocked by the sad news saying "Rhodri was the most popular politician of his generation and the absolute master of the one-liner.
"When Rhodri and I were first elected in 1987 we were part of a Welsh resurgence of political radicalism which was a staging point for 1997 and the road to devolution which has been so crucial to the Wales in which we now live.
"He led the Welsh government and the Assembly through turbulent times to stability and laid the firm foundations on which Carwyn Jones and the current government have been able to build.
"While we had our disagreements, for instance over the Cardiff Bay Barrage, Rhodri was always a vigorous and colourful debater, but not personal. We remained friends and he is someone whose commitment to Wales and to the people he served in Westminster and then in the Assembly was always absolute.
"He will be greatly missed and our sympathy goes to Julie and Rhodri's whole family."
Rhodri Morgan became Chancellor of Swansea University in 2011. He had a great affection for the University, and often joked that without it he would never have been born, as his parents first met as Swansea undergraduates. Many former students have fond memories of him chatting to them when he presented their degree certificates at graduation ceremonies. And of course, as an ardent sports fan, Rhodri enjoyed the annual Varsity rugby match!
Professor Richard B. Davies, Swansea Vice-Chancellor, said: "Swansea University, staff and students, have lost a respected and caring friend who will be greatly missed. Our thoughts are with Julie his wife, their children and grandchildren, and his brother Prys.
"He had an evident affection for Swansea University and was delighted to renew his strong family connections with the University when he became Chancellor in 2011. He embraced the role of Chancellor wholeheartedly. He was in his element presiding over degree ceremonies, chatting with the Graduates, recipients of honorary degrees, and their families. Many events were enlivened by his insightful, entertaining, and often challenging contributions. He was also active as an ambassador for the University in Wales, and overseas he helped promote research collaboration and student exchange programmes. He had an infectious enthusiasm for life and education. The warmth he felt for the University, Swansea, and his country Wales was always evident in his conversations and in his demeanour".