The municipality (originally the parish) is named after the old Skedsmo farm (Old Norse: Skeiðsmór), since the first church was built here. The first element is the genitive case of skeið which means "running track for horse racing" and the last element is mór which means "heath" or "moor".
The coat-of-arms is from modern times. They were granted on 4 October 1974. The arms show three silver horse heads with waving manes on a red background. The arms are canting from the old Norse word skeiðismór which means a field used for horse racing, hence the waving manes of the horses. The arms were designed by Finn Fagerli from Lillestrøm.
Skedsmo was established as a municipality on 1 January 1838 (see formannskapsdistrikt). Lørenskog and Lillestrøm was separated from Skedsmo as municipalities of their own on 1 January 1908. Lillestrøm was, however, merged back into the municipality of Skedsmo on 1 January 1962.
In this area, the tribe of Raumas fought against King Olav Haraldsson, patron saint of Norway, in 1028. The area has become an important part of Norway's industrial history. Strømmens Værksted built the country's first trains, at Kjeller airplanes were constructed up to World War II, the sawmills at Lillestrøm processed lumber from the great forests, and a number of other entreprises have been important.