Bjarni was born to Herjólfr son of Bárdi Herjólfsson (Old Norse: Bárði), and Thorgerdr (Old Norse: Þorgerðr) in Iceland. In adulthood, Bjarni became a merchant captain, based in Norway, but visiting his father every summer in Iceland.
Discovery of America
Bjarni is believed to have been the first European to see North America. The Grœnlendinga saga (Greenlanders Saga) tells that one year he sailed to Iceland to visit his parents as usual, only to find that his father had gone with Erik the Red to Greenland. So he took his crew and set off to find him. But in that summer of 986, Bjarni, who had no map or compass, was blown off course by a storm. He saw a piece of land that was not Greenland. It was covered with trees and mountains and although his crew begged him to, he refused to stop and look around. Since no one in his crew had been to Greenland before, they had to search for it. Although he managed to regain his course, he reported seeing low-lying hills covered with forests some distance farther to the west. The land looked hospitable, but Bjarni was eager to reach Greenland to see his parents and did not land and explore the new lands. Eventually arriving in Greenland, he decided to settle with his father in Herjolfsnes. He reported his findings in Greenland but no one showed much interest in them until, after his father's death, he returned to Norway.
After his voyage, word spread of the lands to the west he had seen, creating great intrigue throughout the Nordic Empire. Bjarni was both celebrated for his discoveries and chided - famously by King Eric - for his lack of investigation. Professor T. J. Oleson of the University of Manitoba stated "There are strong arguments for the view that the three lands seen by Bjarni were Newfoundland, Labrador, and Baffin Island." 
Greenlanders took special interest in his discoveries, and, as they lacked timber, became allured by the wooded coastline Bjarni reported sighting. Soon afterwards, Leif Erikson (Old Norse: Leifr Eiríksson), the son of Greenland leader Eric the Red, bought the ship that Bjarni had used for the voyage, hired a crew of 35 people, and set out to retrace Bjarni's journey. The result is thought to be the Viking settlement at L'Anse aux Meadows in Newfoundland. This is the first known attempt at settlement by Europeans on the Americas.
- Sturlason, Snorre. (2004) Heimskringla Or The Lives Of The Norse Kings, Kessinger Publishing. p. 188. ISBN 0-7661-8693-8.
- Sullivan, Steve & Stephen Krensky. (1991) Who Really Discovered America?, Hastingshouse/Daytrips Publ. p. 36. ISBN 0-8038-9306-X.
- (1997) The Encyclopedia of American Facts and Dates 10th Edition, Collins. ISBN 0-06-270192-4.
- Oleson, T.J., "Bjarni, Hejólfsson”, Dictionary of Canadian Biography vol. 1, University of Toronto/Université Laval, 1979, accessed May 16, 2015
- "Tryggvi Julius Oleson (1912-1963)". Manitoba Historical Society. Retrieved January 20, 2016.
- Kudeba, N. (2014, April 19). Chapter 5 – Norse Explorers from Erik the Red to Leif Erikson – Canadian Explorers Archived 2014-05-08 at the Wayback Machine. Retrieved from The History of Canada.accessed August 13, 2006.
- Oleson, Tryggvi J. (1963) The Norsemen in America (Ottawa: Canadian Historical Association)
- Oleson, Tryggvi J. (1968) Early Voyages and Northern Approaches 1000-1632 The Canadian Centenary Series (New York: Oxford University Press)