The existing methods of synthesis of thermoelectric (TE) materials remain constrained to multi-step processes that are time and energy intensive. Here we demonstrate that essentially all compound thermoelectrics can be synthesized in a single-phase form at a minimal cost and on the timescale of seconds using a combustion process called self-propagating high-temperature synthesis. We illustrate this method on Cu2Se and summarize key reaction parameters for other materials. We propose a new empirically based criterion for sustainability of the combustion reaction, where the adiabatic temperature that represents the maximum temperature to which the reacting compact is raised as the combustion wave passes through, must be high enough to melt the lower melting point component. Our work opens a new avenue for ultra-fast, low-cost, large-scale production of TE materials, and provides new insights into combustion process, which greatly broaden the scope of materials that can be successfully synthesized by this technique.