Fossvellir is inland from the farm Mælifell and was a small crofter´s parcel. The first settler was Björn Guðmundsson of Torfastaðir; permission to settle there is dated 11 April 1861. In the parish census that fall, Björn is the farmer there. Fossvellir was the last of seven farms settled in the fifty years marking the settlement of Almenningur and the loss of grazing rights for the church at Hof. Björn paid two sheep to rent the land. The farm was not used after Björn´s death in 1864 and his widow, Ólöf Arngrímsdóttir, quit the farm in 1865. Sources indicate that after the farm was abandoned, this part of Mælifell´s land was called Fossvellir.