Wiley was born in Chippewa Falls, Wisconsin. He received his undergraduate education at Augsburg College in Minnesota and the University of Michigan. He received his law degree from the University of Wisconsin at Madison, Wisconsin in 1907 and was also admitted to the bar the same year. He served as the Chippewa County District Attorney from 1909-1915.

Wiley was the Republican candidate for Governor of Wisconsin in 1936 but his bid failed. Philip La Follette and new Progressive Party, which split from the Republicans in 1934, won the election. In 1938 Wiley was elected to the United States Senate by defeating incumbent United States Senator F. Ryan Duffy. In 1944, he was challenged by Marine Captain Joseph McCarthy in the Republican Party Primary. He defeated McCarthy and went on to win the general election. Wiley was re-elected two more times in 1950 and 1956. In 1962, Wiley lost his bid for a fifth-term to Governor Gaylord Nelson.

Wiley had a distinguished Senate career that included the Chairmanship of both the Foreign Relations and Judiciary Committees.

Wiley died in Germantown, Pennsylvania. His interment is at Forest Hill Cemetery in Chippewa Falls, Wisconsin. During his lifetime he was a member of the Freemasons, the Knights Templar, the Elks Club, the Kiwanis, the Knights of Pythias, the Moose Lodge and the Sons of Norway.