I will present a formulation of gravity as a double copy of gauge theories in the context of the Becchi-Rouet-Stora-Tyutin (BRST) formalism. I will show how this gives an algorithm for consistently mapping gauge choices from Yang-Mills to gravity. Moreover, it resolves the issue of the dilaton degree of freedom arising in the double copy, thus allowing for the consistent construction of solutions in General Relativity. I will describe the perturbative construction at higher orders. I will also give a formulation of the BRST double copy in a spherical background.