Thermoelectric energy recovery is an important technology for recovering waste thermal energy in high-temperature industrial, transportation and military energy systems. Thermoelectric (TE) power systems in these applications require high performance hot-side and cold-side heat exchangers to provide the critical temperature differential and transfer the required thermal energy to create the power output. Hot-side and cold-side heat exchanger performance is typically characterized by hot-side and cold-side thermal resistances, Rh,th and Rc,th, respectively. Heat exchanger performance determines the hot-side temperature, Th, and cold-side temperature, Tc, conditions when operating in energy recovery environments with available temperature differentials characterized by exhaust temperatures, Texh, and ambient temperature, Tamb. This work analytically defined a crucially important design relationship between (P/Pmax) and (Rh,th / Rc,th) in TE power generation systems to determine the optimum ratio of (Rh,th / Rc,th) maximizing TE system power. A sophisticated integrated TE device / heat exchanger analysis was used, which simultaneously integrates hot- and cold-side heat exchanger models with TE device optimization models incorporating temperature-dependent TE material properties for p-type and n-type materials, thermal and electrical contact resistances, and hot side and cold side heat loss factors. This work examined the (P/Pmax) - (Rh,th / Rc,th) relationship for system designs employing single-material and segmented-material TE couple legs with various TE material combinations, including bismuth telluride alloys, skutterudite compounds, and skutterudite / bismuth telluride segmented combinations. This work defined the non-dimensional functional relationships and found the optimum thermal resistance condition: (Rh,th / Rc,th)opt > 10 to 30 created the maximum power output in TE optimized designs for various TE material combinations investigated. The non-dimensional relationships were investigated for various electrical contact resistances, differing thermal loss factors, and at various hot-side/cold-side temperature conditions. This work showed that the non-dimensional functional relationships were invariant under these differing conditions. It was determined that a condition of (Rh,th / Rc,th) = 1 creates power output far below maximum power conditions. The (P/Pmax) - (Rh,th / Rc,th) relationship also dictated certain temperature profile conditions, defined by the parameter, (Th – Tc) / (Texh – Tamb), which were directly associated with design points in this relationship including maximum power points. The value of (Th – Tc) / (Texh – Tamb) was generally less than 0.5 at maximum power conditions in TE energy recovery designs using TE materials investigated here. The wide-ranging ramifications on TE energy recovery systems and their design optimization for industrial and transportation-related applications are discussed.