Bjarni was born in Upsum at Eyjafjörður to Páll Bjarnason and Sigríður Ásmundsdóttir.
[1] From 1752 to 1757 he traveled around the country with his friend Eggert Ólafsson on a grant from the Danish state.
A book that they subsequently wrote about the trip was published in 1772 under the title Journey through Iceland.
The book was translated into German, French and English in the 19th century, but was not published until 1943 in Icelandic under the title Ferðabók Eggerts og Bjarna.
[2] Bjarni was appointed Iceland's first Director of Health on March 18 1760 by a royal decree.