He moved from the Iceland to Netherlands in 1997 to study sonology at the Royal Conservatory in The Hague with fellow members of experimental trio Stilluppsteypa, which he founded in 1992. After that Bjorgulfsson moved to Amsterdam, where he got a BFA from Gerrit Rietveld Academy and MFA from the Sandberg Institute.
He was a member of Stilluppsteypa for a decade, and together they produced 19 albums and toured all over Europe and in United States. In 2002 Heimir left the band to pursue other projects. Later he was a member of experimental improvisation band The Vacuum Boys and produced two releases with them. He also released nine albums, including a few in collaboration with Jonas Ohlsson on such labels as ERS, Ritornell, Staalplaat, Bottrop-Boy, Crónica.
Bjorgulfsson ran a Fire Inc. record label in 1993-2003, where he put over 20 releases by Stilluppsteypa, The Hafler Trio, Akira Yamamichi, Stock, Hausen & Walkman, Vindva Mei, irr. app. (ext.), Skúli Sverrisson, Carl Michael Von Hausswolff and others.
As a painter and visual artist, Björgúlfsson was exhibited over the years in solo and group exhibitions throughout Europe and USA, at The Living Art Museum and Kópavogur Art Museum in Iceland, Reykjavík Art Museum, Fries Museum, W139 and Gemeente Museum at The Netherlands, Biennale for International Light Art in Ruhr, Germany, Stenersen Museum at Oslo and Museum of Fine Arts, Houston.