Green was born in Jackson County, Wisconsin, the oldest of eight children. He family emigrated to Dakota Territory and settled in Hamlin County in the spring of 1881. Green grew up there and went into the farming business. He served in several local offices including twelve years as president of the local school board. He married Elizabeth Jane Parliament in 1899. They had four children.
Green served three terms in the state senate, South Dakota Legislature. He was elected in 1906, 1922 and 1924. He served on the South Dakota Board of Charities and Corrections from 1913 to 1920.
Green was elected Governor in 1930 and took office at the beginning of the Great Depression. He inherited a massive state debt that he met with tax reform, budget reductions and the reorganization of the state's relief agencies. He reduced salaries from 10 to 20 percent and also had to deal with drought, a grasshopper plague, a crop failure and an exceptionally hard failure. He sought re-election in 1932 by was defeated by Tom Berry.