[1] Simpson was born in Jackson, Teton County, Wyoming, the son of Margaret Louise Burnett (maiden; 1874–1974) and W.L.

[4] As one of fifteen graduates, he was awarded Best All-Round Athlete for his outstanding performance on the school's football, basketball, and baseball teams.

Simpson was in the same class as W. Edwards Deming (1900–1993),[6][7] credited for, among other things, launching the Total Quality Management movement.

He was also in the same fraternity, Alpha Tau Omega, as Glenn Parker (1898–1989),[6][7] whom he appointed to the Wyoming Supreme Court when he became Governor in 1955.

He was a member of the National Association of Governing Boards of State Universities and Allied Institutions and served as president of the body from 1952 to 1953.

Simpson won a special election on November 6, 1962, to the United States Senate to fill the vacancy caused by the death of Republican Senator-elect Edwin Keith Thomson in the term ending January 3, 1967;[10] he was not a candidate for Senate reelection in 1966 but was succeeded by outgoing Governor Clifford Hansen of Jackson.

As governor, Simpson advocated for, and signed into law the Wyoming Civil Rights Act of 1957, a measure aimed at abolishing racial segregation in the state.

Senator, Simpson was one of six Republicans – the others being Barry Goldwater of Arizona, Norris Cotton of New Hampshire, Bourke B. Hickenlooper of Iowa, Edwin Mechem of New Mexico, and John Tower of Texas – who voted against the Civil Rights Act of 1964.

The younger son, Alan K. Simpson, served in the Wyoming House from Park County from 1965 to 1977 and in the United States Senate as a Republican from 1979 to 1997.