Harmeson was a high school star in basketball, football, and baseball for Indianapolis' Emmerich Manual High School; he was awarded three varsity letters in each of three high school sports and was a three-time All-State basketball player.
During his intercollegiate career at Purdue, Harmeson was named all-Big Ten Conference in basketball, football, and baseball; he was a co-captain for the 1930 Big Ten champion basketball team with Stretch Murphy and a teammate of John Wooden and was a member of the 1928 Big Ten champions. He led the Boilermakers to the 1929 Big Ten title in football, quarterbacking them to a perfect record of 8–0 (5–0 in conference), outscoring the opposition 187–44. He was the first Purdue athlete to play on two teams in same academic year that posted undefeated conference marks. As a freshman at Purdue, he was awarded four freshman letters.
He was inducted into the Indiana Basketball Hall of Fame in 1981.
Harmeson was the 18th head football coach for the Lehigh Engineers, now the Lehigh Mountain Hawks, in Bethlehem, Pennsylvania and he held that position for eight seasons, from 1934 until 1941. His overall coaching record at Lehigh was 23 wins, 42 losses, and 5 ties. This ranks him ninth at Lehigh in terms of total wins and 18th at Lehigh in terms of winning percentage.
Harmeson's next coaching move was to become the 23rd head coach for the Wabash College Little Giants located in Crawfordsville, Indiana and he held that position for five seasons, from 1946 until 1950. His coaching record at Wabash was 25 wins, 10 losses, and 6 ties. This ranks him eighth at Wabash in total wins and sixth at Wabash in winning percentage (.683).