Approximately fifty families first established homes in 1875 near the Fremont River. After residents moved to the townsite from 1895 to 1897 the population increased; it was 327 inhabitants from approximately 120 families in the 1990 census.

Once named Thurber after early settler and explorer Albert King Thurber, the settlement experienced a name change in 1916 when Thomas Bicknell, a prominent educator and historian of Providence, Rhode Island, offered a library of 1,000 books to any town that would take his name. The citizens of Thurber voted to accept the library along with Bicknell's name and recorded the action in April 1916. The town was incorporated in February 1939.

Bicknell lies southwest of Thousand Lake Mountain and gradually slopes toward the Fremont River. The townsite was moved to a higher elevation in 1895 to assure a more adequate water supply. Following the advice of the LDS Church, another site was chosen and surveyed, blocks were laid out, and it was dedicated on 7 June 1895.

Residents had to build houses on the new site and did not begin moving in until about 1897. Once established, the citizens were faced with the immediate problem of obtaining culinary water. Pipe was purchased and a new water line constructed from Cotton Wood Springs to the townsite. The pipeline was completed in 1899 with additional water augmenting the system from Durfey Spring. In 1909 a waterworks corporation, the first in Wayne County, was created to maintain the water system. As the population of the town increased, an entirely new line was constructed, bringing water from Jackson Spring.

The school system had an early beginning in Bicknell. The first school opened in 1880 and was taught in the "Herd House" by Hiley Burgess. During the year 1881-82 a combination schoolhouse-dance hall was constructed. In 1890 a frame schoolhouse was constructed, and a rock schoolhouse was finished in 1909. Today the high school for Wayne County is located in Bicknell with students bused to school from the outlying communities in the county.

Bicknell recently has worked at an extensive beautification project. The city has added curb and gutter and sidewalks, and created three mini-parks. The city has received recognition for its efforts by being named "Tidy Town of Utah" in 1984, "Tree City USA," and "Most Beautiful Town" in Wayne County.