Quie was born on his family's farm near Dennison, Minnesota. Quie served in the United States Navy during World War II. He graduated from St. Olaf College in 1950 with a degree in politicial science.
He served in the Minnesota State Senate from 1954 to 1958. He served in the US House of Representatives from February 18, 1958 to January 3, 1979. He was the 35th governor of Minnesota from January 4, 1979 to January 3,1983 and is a member of the Republican Party.