Finley graduated from Fayette County High School and earned his bachelor's degree at the University of Tennessee. After graduating he took assistant coaching jobs at Walker High School and back home at Fayette County before he took the job of head basketball coach and assistant to football coach Larry Wilson at Berry in 1963.
In 1966 Wilson resigned and Wayne Sims took over as head coach. After two lackluster seasons, Sims left and Finley was chosen to take over. His first team went 9-2 in his first year, and his second team entered the 1969 4A state championship game undefeated, but lost to Lee-Montgomery to finish 11-1. The Buccaneers went on to win state championships in 1977 and 1982 (shared with Enterprise after the final game ended in a 10-10 tie). Berry was a runner-up to Vigor High School in 1988. He also coached the girls' basketball team to numerous playoff appearances.
Throughout his career, Finley insisted that his players and students dedicate themselves to representing the school and themselves with dignity. He aimed to set a personal example, and illustrated his lessons with copies of an Ann Landers newspaper column entitled "Class".
Berry's football stadium was named in his honor in 1979. He was inducted into the AHSAA Coaches' Hall of Fame in 1992. After his death a group of former players formed the Robert O. Finley III Foundation which funds scholarships. Hoover High School also gives out an annual award to a student or staff member that exemplifies Finley's values. Hoover's sports and events center at the Hoover Metropolitan Complex was named in his memory in 2016.
- Wood, Wayne (2003) Bob Finley: A Class Act; the Life and Influence of a Great Coach and Teacher. Finley Company ISBN 0974583502
- Bob Finley at ahsfhs.org