The origin of the distinguished Gustafson family can be traced to the historic Scandinavian country of Sweden. The surname Gustafson is derived from the Old Norse personal name Gustav. This name is composed of the tribal name Gaut and the word staf, which means staff or cudgel. The tribal name is thought by experts to be identical with that of the Geats, the Scandinavian tribe to which Beowulf belonged, and it is also thought to be akin to that of the Goths. Thus, the name Gustav literally means staff of the Geats or staff of the Goths. The suffix -sen and its variants are translatable as son of.
In the United States, the name Gustafson is the 1,433rd most popular surname with an estimated 22,383 people with that name. 
^ Filby, P. William, Meyer, Mary K., Passenger and immigration lists index : a guide to published arrival records of about 500,000 passengers who came to the United States and Canada in the seventeenth, eighteenth, and nineteenth centuries. 1982-1985 Cumulated Supplements in Four Volumes Detroit, Mich. : Gale Research Co., 1985, Print (ISBN 0-8103-1795-8)