Haukur was born in Reykjavík on 4 July 1937. He worked as a sailor for ten years and then studied at the Icelandic College of Art and Crafts. He moved to Copenhagen but returned to Iceland where he worked in advertising. In 1977 he designed the board game Útvegsspilið together with Tómas Tómasson and Jón Jónsson.
In the game, players compete by earning money in the fishing industry. The game became a big success in Iceland.
His first art exhibition was in Gallery Djupið in Reykjavík in 1978 with Einar Þorsteinn Ásgeirsson. His first solo exhibition was in Reykjavík in 1980 in Gallery Torg run by the composer Jóhann G. Jóhannson. Since then he has made numerous exhibitions in Europe, China and in the USA. He works in various media, painting, sculpture, jewel making and explores most any media.
Halldorsson explored for a long time the theme of the folklore of his home country Iceland, the Brothers Grimm, Celtic mythology and Nordic mythology in his art practice. He has made numerous drawings an illustrations on the subjects.
Halldórsson has traveled widely to examine art, to China, various countries in Europe, and the United States. In New Mexico, he encountered the Navajo nation and observed the art of sand-casting which he later applied in his own art practice.
His selection of works from 1989 until 2001 combines disparate elements from the worlds of fantasy, myth and everyday experience. His paintings often contain mysterious magical characters, fire-spewing primeval titans, sections of peculiar structures, living skulls, Viking ships in strange surroundings, etc.
Much of his practice revolves the North-European mythology and Nordic mythology. He has gathered information about historical pagan European calendars and myths associated with different parts of the year, which has been the basis for some of his works.
One of his most famous works is the Arctic Henge (Heimskautsgerðið), a series of circles and basalt columns that began its construction in 2004 at the village Raufarhöfn in northeastern Iceland. It has a diameter of 52 meters and works as a complex sundial with numerous references to Norse mythology.