Born 1818 in Copenhagen, the son of a Royal Customs Officer. He abandoned his studies at ship-building school to attend the Royal Danish Academy of Fine Arts for a year in 1838. Both his brothers, Vilhelm and Fritz, were also artists. By 1840 he had exhibited a number of maritime scenes to growing acclaim and was invited to accompany King Christian VIII on a voyage through the Baltic and North Seas. His painting of Eddystone Lighthouse was purchased for the Royal Collection. He went to Paris where he met Corot who influenced Melbye in his use of dramatic light in his paintings. Melbye particularly liked painting stormy weather, but his paintings remain realistic.

In his later years, he travelled between Paris, Copenhagen and Hamburg.

Signed and dated 1863