Not much of his early life is known. He completed his studies in 1919. Icelandic architect Pétur Ármannsson describes him as a dominant figure in Icelandic architecture during the 1920s. During this time, Guðjón was commissioned to plan the major buildings constructed by the Icelandic state. He played a key role in the urban planning of Reykjavík, just as Iceland was urbanizing and modernizing. He tried to create an Icelandic style of architecture. Many of his designs were said to be inspired by the natural geology of Iceland. Guðjón's design of Hallgrímskirkja was, for instance, inspired by basalt columns, such as those at Svartifoss. Guðjón characterized his design of the main-building of the University of Iceland as a distinct and new Icelandic style that he believed would contribute to the revival of the Icelandic Commonwealth. When the British occupied Iceland in 1940, the British commander reportedly opted not to seize the University of Iceland main-building because he considered it too beautiful. His architecture for rural areas, such as the Héraðsskólinn school house, was inspired by Icelandic turf houses. Attempts to re-introduce turf house style buildings to rural areas ended in the 1930s, as these buildings were neither deemed cost-effective nor useful. Guðjón, for instance, opted not for the turf house style when he designed the school house at Reykholt. Many Icelandic church designs are influenced by those of Guðjón, and blend naturalism with modernism.
The house in the corner Austurstræti / Pósthússtræti, Reykjavík, built in 1916/1917, is the first large building in Iceland. it was influenced by Art Nouveau and Danish Nationalist Romanticism and ornated with statues by Einar Jónsson. Inside the building, there was an agency of Landsbankinn and the Reykjavíkurapótek that opened in 1930. After its closure, the restaurant Apótekið moved in
Landspítalinn
Hótel Borg
Héraðsskólinn school house. Constructed in 1928, the school has since been converted into a hostel. Guðjón chose the location for the school house; he chose this particular location due to the nearby hot spring and due to the pleasant scenery.