A painter, Bellany was born in 1942 in Port Seton, East Lothian, Scotland, UK. From 1960-1965, he studied painting at the Edinburgh College of Art under Sir Robin Phillipson and in 1962 was granted the Andrew Grant Scholarship which took him to Paris. He received a Postgraduate Travelling Scholarship in 1965 which enabled him to travel to Belgium and Holland. From 1965-1968, Bellany studied under Carel Weight and Peter de Francia at the Royal College of Art in London.
Bellany became a Lecturer in Painting at Brighton College of Art in 1968 and at Winchester College of Art from 1969-1973, a Visiting Lecturer at the Royal College of Art and at Goldsmiths College of Art. He was Artist in Residence at Victoria College of the Arts in Melbourne in 1983.
Bellany's awards are numerous, among them the Burston Award at the Royal College of Art in 1965, the Major Arts Council Award in 1981 and the Royal Academy's Wollaston Award in 1987.
Bellany's first solo exhibition was held at the Dromidaris Gallery in Holland in 1965 and since 1970, he has exhibited annually throughout the U.K. He was commissioned by the National Portrait Gallery of London to paint a portrait of Ian Botham and in 1968, he was given the first one-man show ever to be held at the NPG.