Prof Thomas, from Blaenau Ffestiniog, Gwynedd, was Emeritus Professor of Welsh at Bangor University.
He published numerous volumes of poetry, was a literary and cultural critic and also translated the mythical Mabinogion stories into English. He also helped pioneer techniques to combine poetry and film.
Prof Thomas leaves a wife and three children.
Gillian Clarke, the current National Poet of Wales, said she was "so sorry" her predecessor "has gone".
"He could not have been kinder, more welcoming or more helpful to me when I followed him into the role in 2008," she said.
Former culture minister Alun Ffred Jones, who was one of his former students, said he was "deeply saddened" by the news.
"Wales has lost a talented scholar and a truly kind man," he said.
"He made a tremendous contribution, not only as a poet but also as someone with the ability to interpret literature to a contemporary audience."
Bangor University paid its own tributes to Prof Thomas, who spent nearly four decades teaching there.
"Wales has lost one of her leading poets and most highly respected academics," said Prof Gerwyn Wiliams, who heads the School of Welsh.
"His contribution to Welsh literature and its study was enormous. He was undoubtedly, one of the most important poets of the second half of the twentieth century, as an innovative poet."
The former National Poet of Wales and academic Gwyn Thomas has died, aged 79.