Djurhuus' parents were Óla Jákup Djurhuus and Else Marienée Poulsen, from Hósvík. He was a great-grandson of Jens Christian Djurhuus. Djurhuus said that his "poetic baptism" came in school, when he heard Jákup Dahl declaim Jóannes Patursson's Nú er tann stundin komin til handa, the anthem of the Christmas Meeting of 1888 which began the rise of Faroese nationalism. Djurhuus trained as a lawyer. After passing the preliminary examinations in 1897, he went to Denmark for university preparation, first in Copenhagen and then in Bornholm. He passed the qualifying examinations in 1900, graduated with the cand. jur.degree in 1911, and then practised in Copenhagen until the late 1930s, when he returned to the Faroes to practise there. However, he kept in touch with his homeland through students. His first published poem was "Blíð er summarnátt á Føroya landi", in 1901. In 1914 he published Yrkingar, the first collection of a single poet's work published in Faroese. He published four further collections of poems. Djurhuus had also studied classical philology, and also published accomplished Faroese translations of Ancient Greek and Latin works, including some of Plato's Dialogues and poetry by Sappho, and a poetic translation of the Iliad.. There is a story that on one occasion when a Greek steamer called at Tórshavn, he went on board and sent a cabin boy for the captain. On his arrival, he began to recite the Odyssey in Ancient Greek. The astonished captain joined in. His poetry combines Classical and Norse mythology. The language of his poems draws on both modern Faroese and the language of the traditional ballads, as well as ancient and modern poetry in other Scandinavian languages; their rhythm is also influenced by ancient Greek and modern German poetry.
Literary reputation
Djurhuus' poetry represented the breakthrough into modern literature in Faroese. His poetry has been judged "among the best" of modern Scandinavian writing, "splendid... of great vision and musicality" and some consider him the greatest Faroese poet, "the first Faroese writer of genius", "without a doubt a great poet". He was a national romantic, but his works show what has been described as poetic idealisation and love of his homeland conflicting with "something of a revulsion from reality" and as "doubt and pessimism, a result of the clash between powerful, pathetic dream of beauty and petty, miserable reality". "Útlegd" is an example of this pessimism.
On 20 September 2004, the Faroese post office honoured Djurhuus with a block of ten stamps, designed by Anker Eli Petersen, depicting ten of his poems. It was chosen as the popular favourite amongst their stamp issues for the year.