At a young age Einar proved himself to be an unusual child with an artistic bent. At that time there was little or no tradition of sculpture in Iceland, so Einar moved to Denmark where he attended the Copenhagen Academy of Art. In 1902 the Althing, the Icelandic parliament, awarded Einar a grant to study in Rome for 2 years. He returned from Rome to Copenhagen and settled down there. According to The Einar Jónsson Museum in Reykjavik, after residing in Rome:
In 1909, after living abroad for almost 20 years he made an arrangement with the Althing to provide him with a home and studio in Reykjavík. In return, he agreed to donate all his works to the country. Einar designed this combination living and working space in collaboration with Architect Einar Erlendsson, though early plans for the house were designed for him by Iceland's State Architect, Guðjón Samúelsson, but these were never realised.
In 1917, the day after he married Anne Marie Jørgensen, he and his bride travelled to the United States to complete the work, and today Einar's intrepid Norseman stands on East River Drive in Philadelphia. Several years later, in 1921, his second major North American work was erected when the Icelandic community in Manitoba, Canada purchased a casting of his Jón Sigurðsson statue and had it placed in the Manitoba Legislative Building grounds in Winnipeg. As with the version in Reykjavík, this statue included the bas relief The Pioneers on the base.
In 1914 Einar was awarded a commission by Joseph Bunford Samuel to create a statue of Icelandic Explorer Þorfinnur Karlsefni (Thorfinn Karlsefni) for placement in Philadelphia. Bunford commissioned the sculpture through a bequest that his wife, Ellen Phillips Samuel, made to the Fairmount Park Art Association (now the Association for Public Art), specifying that the funds were to be used to create a series of sculptures “emblematic of the history of America.” Thorfinn Karlsefni (1915–1918) was installed along Philadelphia's Kelly Drive near the Samuel Memorial and unveiled on November 20, 1920. There is another casting of the statue in Reykjavík, Iceland.
In recent years Einar's plasters have been cast in bronze and placed in the garden of his home and studio or in city parks in Reykjavík and throughout Iceland. He donated his work to the Einar Jónsson Museum in Reykjavík, which opened in 1923.