The first town formation known in North Norway, Vågar, was situated around the narrow, natural harbor near Kabelvåg, just west of Svolvær. Vågar is mentioned in the book Heimskringla, and might have been established as early as the year 800 AD.

Atlantic Cod fisheries, particularly during winter months, have remained one of the most important economical foundations for the town. Other industries which have proved to be valuable resources for Vågan are fish farming (salmon), Secora and Lofotkraft.

Svolvær's historical significance as an important fishing village allowed the town to be granted town status (ladested) on 1 July 1918 when the new town of Svolvær was separated from the municipality of Vågan to become its own municipality. Initially, the new municipality had 2,429 residents and it included 7.3 square kilometres (2.8 sq mi) of land. During the 1960s, there were many municipal mergers across Norway due to the work of the Schei Committee. On 1 January 1964, Svolvær municipality was merged with the municipalities of Gimsøy and Vågan to form the new, larger municipality of Vågan as it is known today. Prior to the merger, Svolvær had 3,952 residents. Due to this merger, Svolvær lost its status as a "town".[1][2]

Following new legislation, Svolvær was again able to declare itself a "town" in 1996.

The town (and former municipality) is named after the old Svolvær farm (Old Norse: Svǫlver) since the town grew up on the site of the historic farm. In 1567, historical records show the name as "Suoluer". The first element of the name comes from the word svalr which means "cool" or "chilly". The last element is vær which means "fishing village".[3]

The coat of arms was granted on 20 January 1941 and it was in use until 1964 when it became part of Vågan Municipality. The official blazon is "Azure, a cod naiant argent in between a bar gemel wavy" (Norwegian: På blå bunn en vannrett sølv torsk mellom to bølgede strenger av sølv). This means the arms have a blue field (background) and the charge is a cod in between two wavy lines. The cod and wavy lines both have a tincture of argent which means it is commonly colored white, but if it is made out of metal, then silver is used. The blue color and the design of the arms symbolize the importance of the sea and fishing for the municipality. The arms were designed by John Johnsen.[4][5]

Svolvær was a municipality from 1916 until 1964, and during that time, it was self-governing as a municipality. During this time, it was responsible for primary education (through 10th grade), outpatient health services, senior citizen services, unemployment, social services, zoning, economic development, and municipal roads. During its existence, this municipality was governed by a municipal council of elected representatives, which in turn elected a mayor.[6]

The municipal council (Bystyre) of Svolvær was made up of representatives that were elected to four year terms. The party breakdown of the final municipal council was as follows: