Kelley graduated from Cornell University in 1941 after playing three seasons of football under Carl Snavely and fellow fraternity brother George K. James, including the 1939 undefeated national championship season. He was a member of Sphinx Head, the Phi Kappa Psi Fraternity, and through the latter organization, the Irving Literary Society. He was assistant coach at Cornell from 1946 to 1949, before becoming head coach at Brown University and then Colgate. He was inducted into the Cornell Athletic Hall of Fame in 1980.
Kelley was the 27th head football coach at Colgate University, serving for three seasons, from 1959 to 1961, and compiling a record of 9–18.
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