Mr Dunn, a protege of the poet Philip Larkin, was recognised for his body of work spanning more than four decades.
Poet laureate Carol Ann Duffy, who chaired the medal's judging committee, said: "Douglas Dunn's sparkling, erudite and distinguished body of work has long been one of the grace notes of British poetry.
"He stands deservedly among the greatest poets that Scotland has produced."
The committee was unanimous in recommending Mr Dunn as this year's recipient of the award, on the basis of a lifetime's contribution to literature, and his distinguished output as a poet.
The poet studied at Hull university and also worked at the institution's library below Philip Larkin, a major influence on his career.
The honour is awarded for excellence in poetry for a body of work or an outstanding poetry collection published during the year of the award. The Queen will present the medal next year.