Wyatt was born in Louisville in 1905 and attended the University of Louisville as well as the Jefferson School of Law, becoming an attorney in 1927. He was the principal counsel for The Courier-Journal and other Bingham family owned media companies prior to his political career.
Wyatt's political career began with his election as Mayor of Louisville in 1941. He took office just after the bombing of Pearl Harbor ushered America into World War II. Wyatt made civil defense a priority and was involved with a great deal of planning related to that. Wyatt also initiated Louisville's planning and zoning commission.
As his term as mayor of Louisville ended, President Harry S. Truman appointed Wyatt as United States Housing Expediter for the Office of War Mobilization, a position that was given cabinet-level rank.
In 1959 Wyatt planned to run for Governor of Kentucky. He eventually decided to run for Lieutenant Governor with the party's 1955 nominee, Bert T. Combs, at the top of the ticket. Combs and Wyatt were both elected and served in those offices from 1959 through 1963. Combs' administration created the Kentucky Economic Development Commission and Wyatt was its chairman.
In 1963 President John F. Kennedy appointed Wyatt as a special envoy to Indonesia to deal with Indonesian president Sukarno who was threatening to nationalize foreign oil companies there. Wyatt's mission was successful and Sukarno did not nationalize the foreign-owned elements of the Indonesian oil industry.
After leaving the lieutenant governor's office in 1963, Wyatt established the law firm Wyatt, Tarrant & Combs which included Governor Bert Combs with whom Wyatt had served in Frankfort for the preceding four years.
In 1968 Hubert Humphrey, the Vice President of the United States and Democratic presidential nominee, had Wyatt play an important role at the Democratic National Convention in working out a compromise over the party's platform on the Vietnam War.
For the remainder of his life Wyatt was active in the legal community and with civic affairs in Kentucky. He and his wife Anne donated $500,000 to the Jefferson County, Kentucky public schools to create scholarships for high school debaters, and another $500,000 to the law school at the University of Louisville, where he had once served as chairman of the board of trustees. The university in turn named its law school building after Wyatt in 1995. In addition, Wyatt served a term as chairman of the board of trustees at Bellarmine University, and a sizeable donation from him and his wife funds a lecture series at the school.
Wyatt died in 1996; he is interred in Section 33, Lot 13 of Cave Hill Cemetery in Louisville.