An Alabama man named Evant Brooks purchased some of land from Langford in the late 1870s. In 1881, Brooks had donated sixty acres of land "for sale and settlement as a town", and by 1884 the growing community changed its name to Evant in Brooks' honor. In the 1890s, the community had a cotton gin, three general stores, a gristmill, and a hotel. Its population was around 10 residents.
Evant continued to grow, reporting a peak population of 550 sometime in the 1950s. The town was formally incorporated in the mid-1970s. Its population at the time was 540 and has continued to shrink. According to the 1990 census, the town's population was 444, and as of 2005, the census estimates the population at 388.
According to the United States Census Bureau, the town has a total area of 0.6 square miles (1.6 km²), all of it land.
There were 159 households out of which 33.3% had children under the age of 18 living with them, 49.7% were married couples living together, 11.3% had a female householder with no husband present, and 36.5% were non-families. 34.0% of all households were made up of individuals and 20.8% had someone living alone who was 65 years of age or older. The average household size was 2.47 and the average family size was 3.25.
In the town the population was spread out with 31.6% under the age of 18, 4.6% from 18 to 24, 27.2% from 25 to 44, 17.3% from 45 to 64, and 19.3% who were 65 years of age or older. The median age was 36 years. For every 100 females there were 95.5 males. For every 100 females age 18 and over, there were 83.0 males.
The median income for a household in the town was $22,500, and the median income for a family was $30,227. Males had a median income of $23,333 versus $21,250 for females. The per capita income for the town was $12,589. About 14.7% of families and 25.4% of the population were below the poverty line, including 35.7% of those under age 18 and 11.8% of those age 65 or over.