Thomas William Edmondson was born in Skipton-in-Craven, Yorkshire, England, on June 26, 1869. His parents, Sarah Dodgson and Thomas Edmonson, Sr., were middle-class tradespeople. Thomas Edmondson, Sr. had worked himself up through the printing apprentice system and was a master printer in Skipton. He owned a small business, Edmondson & Co., Printers and Stationers, and was very active in civil affairs and the Oddfellows Society. Thomas was one of eight children. He attended elementary school in Skipton. From 1879-1888, he was the recipient of a scholarship at the Skipton Endowed Grammar School. In June 1886, he took the London University matriculation examination. When his results were published, he was first on the Honors List. He took his B.A. at London University in 1888.

In 1887, Edmondson received the Ackroyd Scholarship, which enabled him to attend Pembroke College in Cambridge. The Ackroyd was a senior mathematical scholarship. He received his B.A. from Cambridge in 1891. After getting his degree, he continued at Cambridge as an assistant tutor in mathematics and physics at the University Correspondence College and pursued graduate studies in physics, chemistry, and botany.

During the summer of 1893, he immigrated to America. After a year in the United States, he was appointed to a Fellowship in Physics at Clark University in Worcester, Massachusetts. He was awarded the Ph.D. in 1896 as a result of study and research at Clark.

Following conferral of his degree, Edmondson was appointed Assistant Professor of Physics at NYU's University College, located on the Heights campus in the Bronx. In addition to his work in the Physics Department with Professor Daniel W. Hering, he also assisted Professor Pomeroy Ladue in the Mathematics Department. In 1903, Edmondson became an assistant professor of mathematics. Following Ladue's resignation in 1906, Edmondson was appointed head of the Mathematics Department.

Professor Edmondson also served NYU as an administrator. He was Secretary of the Faculty Committee of the University Council from 1903-1933 and served as Acting Dean of the Graduate School from 1916-1921. He was also chairman of the Washington Square Collegiate Division in 1913. On August 31, 1934, Edmondson's long service to the University formally ended with his retirement. He died on November 4, 1938.

Thomas W. Edmondson was married in 1896 to Minnie Ramsden. They had no children.