He was born in Skagafjörður, Iceland but emigrated to Wisconsin, USA in 1873, when only 19 years old. In 1889 he moved to Markerville, Red Deer County, Alberta, Canada. He did not see Iceland again until 1917, when he was 64 years old.
Stephan was self-educated and worked hard all his life. He wrote after work, and, being an insomniac, he often wrote till dawn. He was under the influence of the American writer Ralph Waldo Emerson and they shared the same beliefs in many matters, including, but not limited to, equal rights for both sexes. Stephan wrote only in Icelandic and had great influence in his former home country.
His poems were published in a six volume book called "Andvökur" (Sleepless Nights).
His homestead near Markerville is an Alberta Provincial Historic Site. It has been restored and is open to the public from May 15 until August 31.