Keaney was a native of Boston, Massachusetts, and attended Cambridge Latin School, graduating in 1906. He graduated from Bates College, where he played several sports, in 1911. He was the head football coach at Everett High School in Massachusetts from 1917 to 1919. He coached at Rhode Island State College (now the University of Rhode Island) from 1920 to 1948 and taught a style of basketball using a fast-breaking offense and a full-court defense. In his 28 years at Rhode Island, Keaney's basketball Rams won 8 conference championships and had only one losing season. In 1939, Keaney's Rams became the first college team to score more than 50 points per game, and in 1943 the team had an average of more than two points per minute (80.7 points per game), which led to the Rams being dubbed "The Firehouse Gang". During his tenure the URI team had four National Invitation Tournament appearances. Keaney's career record with the men's basketball team was 401-124 (.764).
After retiring from coaching collegiate basketball, Keaney was offered the position of head coach of the Boston Celtics. Keaney's doctor, however, refused to let him take the job. He remained at URI as athletic director until 1959. The university named the Frank W. Keaney Gymnasium-Armory in his honor in 1953. Keaney was inducted into the Basketball Hall of Fame in 1960.
- Klein, Maury (November 27, 1978). "Yesterday Frank Keaney invented the fast break and Rhode Island made the big time". Sports Illustrated. Retrieved November 9, 2014.
- Karsten, James (October 8, 2014). "Top 10 Bates Athletes: #7 Frank Keaney '11". The Bates Student. Retrieved November 9, 2014.
- "Frank Keaney Coaching Record". College Basketball at Sports-Reference.com. Sports Reference. Retrieved November 9, 2014.
- "Hall of Famers - Frank Keaney". Naismith Memorial Basketball Hall of Fame. Retrieved November 9, 2014.