Mosaic artist Ed Chapman used stone from the disused Rhiwbach Quarry, in Conwy, to make the piece.
It has been created to mark what would have been Mr Burton's 90th birthday this month.
The mosaic is expected to find a permanent home at Swansea University, close to the Pontrhydfen birthplace of Mr Burton who died in 1984 aged 58.
"I have long been a fan of Richard Burton and I wanted to create a unique portrait of him, if possible incorporating something Welsh of which he would be proud and possibly amused," Mr Chapman said.
Mr Burton's fourth and last wife Sally called the artwork "a glorious creation".
A unique portrait of actor Richard Burton has been made using 500 million-year-old slate from Conwy county.