The surname "Fossberg" in Norwegian is the same as the surname "Forsberg" in Swedish, and the Norwegian form "Fossberg" is probably a Norwegification of the Swedish name "Forsberg". On this I am uncertain, but Forsberg is more common in Sweden than Fossberg is in Norway. In my case, my great grandfather came from Sweden to Norway in the 1930's, during the depression, and in order to compete in finding a job, he changed his Swedish name Forsberg to a Norwegian form Fossberg, both meaning the same, but leading prospective employers to consider him among Norwegians rather than a Swede taking jobs from others.
The name is Scandinavian in any case and consists of two parts: "Fors" in Swedish, "Foss" in Norwegian, both the same term for Waterfall. "Berg" is the same in Swedish and Norwegian, meaning Mountain. "Berg" is not uncommon in Norway as a surname on its own. You can confirm this as easily as Google Translate, or any other way.
The origin is likely that a family lived on a mountainside with a waterfall close by. This is common in Sweden and even more Norway. Scandinavia consists of Norway, Sweden and Denmark. The surname is inconceivable in Denmark as the land is flat.