Neely grew up in Tampa, Florida, where he moved to as a child from Mobile, Alabama.

[1] He played collegiate tennis for the University of Florida, earning All-American honors in 1968 and 1969.

During his time at the University of Florida he remained unbeaten in SEC singles dual matches.

[1] A right-handed player, Neely competed on the professional tour in the 1970s and had a career high singles ranking of 144 in the world.

His best grand slam performance came at the 1975 US Open, where he reached the quarter-finals of the men's doubles, partnering Tenny Svensson.