Elwood was originally just a large meadow with beautiful bunch grass that herds of cattle and bands of sheep put to good use in the summer time. In 1868, a Mr. Davidsen and his family used "Squatter's Rights" to take ownership of a tract of land on the banks of the Malad River. Over the next few years more homesteaders arrived and took up residence. In 1889 a branch of the LDS was formed and gave the area the name Fairview. At the same time a post office was applied for. That was when the postal service suggested the name of Elwood (because there was already a Fairview in Utah). Finally, in 1898, a post office in the name of Elwood was established.

In 1891, the community opened a 1-room school in a brick building, then expanded that to 4 rooms in 1917. The Elwood Ward of the LDS Church was established in 1900 but they didn't have a formal meeting place for religious services until 1904 (and even then, the building they used was an amusement hall when it wasn't being a church). 1904-1905 saw the expansion of Bear River Valley telephone service into Elwood. The first electric power line arrived in 1921.

Today, many of the residents of Elwood are direct descendants of those first pioneer families, many of them living on the same properties their forefathers homesteaded and in the same homes they'd built.