Webber was born in Lawton, Michigan on December 27, 1865 the only child of John Milton Webber and Rebecca Ann Bradt. In 1867, the family moved west to Marshalltown, Iowa where they would remain for the next fifteen years before moving on to Lincoln, Nebraska in 1883. On September 8, 1890 Webber married Lucene Anna Hardin. The couple had four children.
Webber attended Willow Hill school followed by the Albion Seminary for his primary school education. He obtained his Bachelor of Science degree in 1889, and his master's degree in 1890 from the University of Nebraska. In 1900, he received his Ph.D. from Washington University in St. Louis.
Beginning in 1892, Webber worked for the United States Department of Agriculture where he investigated orange diseases in Florida and from 1889 to 1907 had charge of the department's plant-breeding investigations. In 1898 Webber represented the USDA in London at the International Conference on Hybidization.
In 1907 Webber, then-considered the "most notable plant breeder and botanist in the USDA," was hired by Liberty Hyde Bailey, dean of Cornell University's New York State College of Agriculture, to serve as professor of experimental plant biology director of the school’s Department of Plant Breeding. Bailey often left Webber in charge of the college while Bailey participated in conferences away from Ithaca before appointing Webber as acting dean in 1910. While at Cornell Webber's stressed biological research with particular focus on both genetics and breeding. He was a partner in the development of several cultivars including Cornell 1777 Timothy grass, Honor Winter Wheat, Cornell Welcome Spring Oats, Weber's Early Dent O.P. Corn, Cornell 11 and 12 Corn, In 1912 Webber went to the University of California to be director of the Citrus Experiment Station, dean of the Graduate School of Tropical Agriculture, and professor of plant breeding. Webber was one of the advocates in 1913 of keeping the station in Riverside rather than re-locating the facility to the San Fernando Valley. Together with Walter Tennyson Swingle he originated citranges, a hardy citrus fruit, by hybridization. In 1915 Webber joined the California Avocado Society, serving as director twice and president once. During 1920 Webber took a sabbatical from University of California to serve as general manager of South Carolina-based Pedigreed Seed Company only to return to the Citrus Experimentation Station the following year. He retired as director of the Experimentation Station in 1929 and retired from teaching in 1936. In 1939, he and Leon Dexter Batchelor discovered an orange cultivar, Olinda Valencia, in Southern California. Webber was a founding member of the Los Angeles Farm Bureau.
Webber had been a member of the American Association for the Advancement of Science, the American Botanical Society, the American Society of Naturalists, the Society of Horticultural Science, the American Genetic Association, and the Ecological Society of America, as well as academic societies Sigma Xi, Alpha Zeta, and Kappa Delta Rho.
Webber coined the word "clone" in 1903 and was the first to use it to describe a colony of organisms derived asexually from a single progenitor.
Webber wrote some 263 publications. He was a contributor and worked on the editorial board of The Citrus Industry. The book has been called the “bible of citrus growers.”"Some facts concerning the New York State College of Agriculture at Cornell University. Presented to a hearing of legislative committees". Albany, New York. April 5, 1910 – via Archive.org.
"The effect of research in genetics on the art of breeding". 1912 – via Archive.org.
Webber was awarded a Doctor of Agriculture degree from University of Nebraska in 1913 and a Doctor of Laws degree from the University of California in 1943. Webber Hall, a life sciences building on University of California, Riverside, was named in his honor.