The 361-square-kilometre (139 sq mi) municipality is the 255th largest by area out of the 422 municipalities in Norway. Sørreisa is the 247th most populous municipality in Norway with a population of 3,496. The municipality's population density is 10.1 inhabitants per square kilometre (26/sq mi) and its population has increased by 5.5% over the last decade.
The municipality of Sørreisen was established on 1 September 1886 when it was separated from the municipality of Tranøy. The initial population of Sørreisen was 1,361. Later the spelling was changed to Sørreisa. On 1 January 1964, the part of Sørreisa across the Reisafjorden on the island of Senja (population: 129) was transferred to the municipality of Lenvik.
The municipality is named after the Reisafjorden (originally Reisa), which again is named after the Reisaelva (the "Reisa river" - originally Reisa). The river name is derived from the verb rísa which means "raise" (referring to flooding). The first element Sør ("south") was added to distinguish the municipality from Nordreisa. The municipality was originally named Sørreisen.
The coat-of-arms is from modern times. They were granted on 7 September 1984. The arms show three gold stars on a red background. It was derived from the oldest known seal in the municipality, a 17th-century seal of Jacob Hansen Kinapel, who was a police sergeant in Sørreisa from 1715 to 1748.