Current's history began with Swift Current Creek which originates at Cypress Hills and traverses 100 miles (160 km) of prairie and empties into the South Saskatchewan River. The creek was a camp for First Nations for centuries. The name of the creek comes from the Cree, who called the South Saskatchewan River Kisiskâciwan, meaning "it flows swiftly". Fur traders found the creek on their westward treks in the 1800s, and called it "rivière au Courant" (lit: "river of the current"). Henri Julien, an artist travelling with the North-West Mounted Police expedition in 1874, referred to it as "Du Courant", and Commissioner George French used "Strong Current Creek" in his diary. While it took another decade before being officially recorded, the area has always been known as "Swift Current".

The settlement of Swift Current was established in 1883, after the CPR surveyed a railway line as far as Swift Current Creek. In 1882, initial grading and track preparation commenced, with the first settlers arriving in the spring of 1883. During the early part of its settlement, the economy was based almost exclusively on serving the new railway buildings and employees. There was also a significant ranching operation known as the "76" ranches. It included 10 ranches raising sheep and cattle and stretched from Swift Current to Calgary. The ranch located at Swift Current dealt with sheep. At one point there were upwards of 20,000 sheep grazing on the present day Kinetic Grounds. The head shepherd was John Oman, originally from Scotland. He donated land to build Oman School in 1913. Other early industries included gathering bison bones for use in fertilizer manufacturing, the making of bone china and sugar refining. Métis residents also ran a successful Red River ox cart "freighting" business to Battleford until the late 1880s. During the Riel Rebellion of 1885, Swift Current became a major military base and troop mustering area due to its proximity to Battleford but this was only for a short time. On February 4, 1904, the hamlet became a village and then a town on March 15, 1907, when a census indicated a population of 550. Swift Current became incorporated as a city on January 15, 1914, with Frank E. West being the mayor at the time.