Born in Milford, Massachusetts, Johnson graduated from Milford High School in 1883, Harvard University with a B.A. in 1887, and Harvard University’s Lawrence Scientific School with a degree in Civil Engineering in 1888. He studied in Europe from 1888 to 1890, the Federal Polytechnic School in Zurich from 1888 to 1889, and the École Nationale des Ponts et Chaussees in Paris from 1889 to 1890. Johnson taught civil engineering at Harvard University in varying capacities between 1890 and 1934. From 1892 to 1894, he practiced in Chicago in association with the Illinois Steel Company. During his time at Harvard University, Johnson sketched a design for Harvard Stadium, proposed the use of large steel-reinforced concrete slabs, and supervised the construction of the stadium with Joseph Worcester in 1903. From 1914 to 1919 Johnson was also a professor of civil engineering at the Massachusetts Institute of Technology (MIT). In 1934 he began lecturing on applied economics and political science at the Division of University Extension at the Massachusetts Department of Education.
Johnson also wrote about technical and civic matters, publishing Statics by Algebraic and Graphic Methods (1903 and 1908) and “Materials and Design of the Harvard Stadium” in the Harvard Engineering Journal (1904). He was a Fellow of the American Academy of Arts and Sciences and a member of the American Society of Civil Engineers, the American Society for Testing Materials, the Boston Society of Civil Engineers, the American Association of University Professors, and the League of Nations Association. Johnson died at the age of 84 and was buried in Pine Grove Cemetery in Milford.