In 1922, the university's Board of Regents ended a contract with nationally-known architect Cass Gilbert, who designed Sutton Hall (1918) and Battle Hall (1911), thus establishing a Spanish-Mediterranean revival style for the campus. Under pressure from the legislature to hire a Texas architect, the regents appointed Greene to replace Gilbert. In 1923, they hired James M. White to develop a campus plan and Robert L. White to supervise construction of Greene's buildings.

During his contract, Greene designed the Texas Memorial Stadium (1924), the Biology Building (1925, now Biological Laboratories), Garrison Hall (1926), Littlefield Women's Dormitory (1927), the Chemistry Building (1931, now Welch Hall), Waggener Hall (1931), the Men's Gymnasium (1930, now Gregory) and the Women's Gymnasium (1931, now Anna Hiss). Because of the high volume of building required by the university, Greene hired several associates over the years, including Edwin B. LaRoche and George L. Dahl. In 1928, the three formed the partnership of Greene, LaRoche and Dahl.

In 1930, dissatisfied with James White's campus plans, the Faculty Building Committee, chaired by William James Battle, hired Paul Philippe Cret of Philadelphia as supervising architect. Cret integrated all of Greene's buildings in his campus plan, using the two Greene-designed gymnasiums as focal points within his designs for men's and women's sections of campus. Beginning in 1931, Greene, LaRoche and Dahl worked with Cret on the demolition of Old Main and the construction of the new main building and tower in its place. That year the firm also built the Architecture Building (now Goldsmith Hall), the Home Economics Building (now Gearing Hall), and the Engineering Building.

Greene died the following year. His firm, Greene, LaRoche and Dahl, continued building with Paul Cret on the UT campus, and eventually formed the partnership of LaRoche and Dahl.