Born in 1869 in Howell, Michigan, Peavy received his Bachelor's degree from the University of Michigan. After teaching history and economics and serving as a high school principal, he became interested in forestry and re-entered the University of Michigan earning a Master of Science degree in Forestry in 1905. In 1910 Peavy was selected to head of the newly created Department of Forestry at Oregon Agricultural College and subsequently served as the first Dean of the School of Forestry from 1913 until his retirement in 1940.
George Peavy was appointed Acting President of Oregon State College in 1932 when President Kerr was chosen as the first Chancellor of the Oregon State System of Higher Education. In January 1934 he was designated President of the College and also continued as Dean of Forestry, positions he held until his retirement in 1940. He lead the institution through the infancy of the Oregon State System of Higher Education, a period of administrative restructuring and limited economic resources. The first Ph.D. degrees were awarded by the College during this time.
After his retirement, Peavy was elected Mayor of Corvallis in 1947, a position he held until his death in 1951.