Turbulence-induced scintillation is the principal impairment to Gbps laser communication over clear-weather atmospheric paths. This paper, plus its companion [A. Puryear, J. H. Shapiro, and R.R. Parenti, "ReciprocityEnhanced Optical Communication through Atmospheric Turbulence-Part II: Communication Architectures and Performance"], introduce and analyze the exploitation of atmospheric reciprocity for combating turbulence. Part I presents reciprocity proofs that apply under rather general conditions and underlie the communication performance analysis in Part II.