Born in Skagen, Brøndum was the son of Erik Andersen Brøndum and Ane Hedvig Møller, who ran the business before him, and the brother of Anna Ancher, who became one of the Skagen painters. He took the hotel over around 1880. He was one of the founders of Skagens Museum in 1908.
An avid art lover, Brøndum provided accommodation for many of the artists who came to spend the summer months in Skagen. In addition to Michael Ancher, who married his sister Anna, the guests included P.S. Krøyer, Christian Krogh, Carl Locher, Holger Drachmann, Agnes and Harald Slott-Møller, Georg Brandes, Thorvald Bindesbøll and Hugo Alfvén. It the artists were short of money, they were able to cover the cost of their board by donating portraits which were hung in the dining-room. When the dining-room became too small to accommodate the increasing number of guests, Brøndum called upon Bindesbøll to design a larger room where the paintings could be hung on the paneling. Degn Brøndum left the dining-room to Skagens Museum where it transferred in 1946.