The origin of the Hofdi house is traced back to the times, when French fishermen frequented the Icelandic fishing grounds in the late 19th and early 20th centuries. The French government posted a consul, Mr. Brillouin, in Reykjavik to assist them. A lot for his abode was procured and the house was imported from Norway. It was one of the many wooden catalog houses built in Iceland in the early 20th century, but probably one of the most beautiful ones. It still bears many signs of its original purpose, such as the letters RF, the abbreviation of the French Republic the name of the consul and the year of its construction above an inside door.

The house is also decorated with the Roman fasces with two axes, signifying the power of the Roman officials to whip or decapitate. The „bonnet rouge", a part of the uniform of the Jaçobins during the French revolution in 1789 also decorates the door frame. The house was among the largest villas of the town and was admired by the people, who saw it. Mr. Brillouin did not fit in and left the country in the beginning of world war I and the house was sold. The buyer was the poet, advocate and entrepreneur Einar Benediktsson. For a period of time the house was occupied by the British Vice Consul and later the British Ambassador to 1951.

The most famous visitor of the Hofdi house is probably Sir. Winston Churchill. He visited Iceland in 1941. Marlene Dietriech also visited the house during the second world war. The last British Ambassador to occupy the house was a bachelor and rather peculiar in his habits. Every day he saw a being of another world roaming about the house. He called it „The White Lady". She tried his nerves so much, that he persuaded the British foreign office to sell the house. Eventually the house became the property of the municipality and was destined for demolition as it had fallen into disrepair.

The municipal architect, however, had it restored secretly and then showed it to the mayor, who was quite satisfied with the results. From then on the house has been used for official receptions and meetings of the municipality. Thousands of renowned guests have honoured the capital with there presence, among them heads of states, the king of Norway, presidents of France, the queens of England and Denmark, the presidents of Italy, chancellor Willy Brandt of Germany and many others. The most renowned guests of the Hofdi house are without a doubt the presidents Ronald Reagan and Mikhail Gorbatsjov, who attended a summit meeting there in October 1986.

During this meeting the house became world known and a Japanese millioner had an exact replica of the house built in his country. The sculpture in front of the house depict the high seat pillars of the first Norwegian settler in Reykjavik.