The first known farmer at Keldur was Ingjaldur Höskuldsson; he is mentioned in the 13th century Njal's saga. The farm later became the residence of the Oddaverjar chieftains. The chief Jón Loftsson lived here and is believed to be buried in the village. In the 13th century, the chieftain Hálfdan Sæmundsson, grandson of Jón, and his wife Steinvör Sighvatsdóttir lived at Keldur.
The foundation of the residential building in Keldur is considered to be from the 11th century. The house is today the oldest in Iceland. The residence is now a museum. From the residential building, an old underground passage leads to the farm stream, which was rediscovered during an archaeological excavation in 1998.[1] Such passages, called jarðhus, are mentioned in the Icelandic sagas.
In the past, the land north of Keldur was an overgrown area with several farms now buried in the black lava sand. The area was overgrown until the middle of the 19th century when the sand took over. The sand is believed to have arisen in connection with the eruption of Hekla in 1511. When the thick layer of pumice settled after the volcanic eruption, south and southwest of Hekla, sand began to blow through wind erosion towards Rangárvellir and the village of Keldur.
There has been a church in Keldur from the earliest times, and served from Odda. The current log church, called Keldnakirkja in Icelandic, was built in 1875.