Elmina Tessa Wilson was born on 29 September 1870 in Harper, Keokuk County, Iowa to Olive (née Eaton) and John C. Wilson. She was the second-to-the-youngest daughter in a family of five other siblings, Warren, Fanny, Olive, Anna, and Alda. In 1892, she graduated from Iowa State University (ISU) with the first four-year civil engineering degree awarded any woman from an American university. In 1894, Elmina graduated with a master's degree in civil engineering from ISU, simultaneously with sister Alda's graduation with a bachelor's in the same field. Both sisters were members of Pi Beta Phi women's fraternity and staunch supporters of both women's education and suffrage.

Design of the Marston Water Tower began in 1895 when a drought caused a severe water shortage. The project lead was Anson Marston, dean of the engineering department at Iowa State University, with Wilson assisting. The design of the 40-foot-tall (12-meter) and 24-foot-diameter (7.3-meter) water tower, included eight columns, rather than the standard four, to safely support the 162,000-gallon structure. It was also the first steel, rather than wood, elevated tower west of the Mississippi River. The tower was listed on the National Register of Historic Places in 1981, three years after it was decommissioned as the water reservoir and pressure regulation system for the campus water supply.

In the fall of 1903, Wilson and her sister Alda took a sabbatical to study engineering and architectural designs in Europe. Traveling mostly on bicycles, they visited England, France, Germany, Greece, Italy, Scotland and Switzerland. Upon their return to the states in 1904, Wright resigned from her post at ISU and sought private employment in New York City with the James E. Brooks Company. Her first assignment with the firm was at the Essex Structural Steel Works in Bloomfield, New Jersey. In 1906, she began working on publications with the U.S. Department of Agriculture and a brochure entitled Modern Conveniences for the Farm Home was serialized in several newspapers nationally. Articles included topics such as piping water pumped by a windmill throughout rural homes or adding bathtubs serviced by water pumped from elevated tanks in an attic or pneumatic cylinders installed in basements,

The following year, Wilson joined the prestigious engineering firm of Purdy and Henderson, Leaders in skyscraper design, where she began work on the Flatiron Building and later worked on the Met Life Tower. In December 1907, the sisters sailed aboard the White Star Line's ship Adriatic, returning to Europe to spend six months studying architecture in France and Spain. Returning home, they worked together on the design of a residence in Ames, Iowa for W. J. Freed and his daughter Kittie. In 1911, Wilson served as President of the New York Chapter of the Pi Beta Phi Alumni Club. Then she was hired as a structural designer in 1912 by the John Severn Brown Company. In 1913, the sisters planned another trip, to study for eight months in Germany, Italy, and Sicily.

In 1909, Wilson and her sister Alda designed a residence for W. J. Freed and his daughter Kittie. The house was a six-room cottage located on Story Street in Ames, Iowa.

Helmich House was designed in 1915 and was the first known architect-designed dwelling in Gatlinburg, Tennessee. It was part of the campus of Arrowmont School, a project promoted by Phi Beta Phi as a settlement house-type program based on the model of the agricultural schools in vogue in the Progressive Era. The ten-room residence was a 1½-story frame bungalow on a concrete foundation. Built in 1916, the residence, which was constructed to provide living quarters for the teachers being recruited to work in the school, had modern amenities including the first furnace in Gatlinburg and running water. The exterior was clad with weatherboard siding featuring shed dormers on the north and rear façades, covered by a side-gabled, asphalt-shingled roof. In 2007, the teacher's residence was placed on the National Register of Historic Places as part of the Settlement School Community Outreach Historic District of Sevier County, Tennessee.

Wilson died on June 4, 1918 in New York City and was buried there.