The authors show that, in a metric space \(X\) with annular convexity, the uniform domains are precisely those Gromov hyperbolic domains whose quasiconformal structure on the boundary agrees with that on the boundary of \(X\). As an application it is shown that quasi-Möbius maps between geodesic spaces with annular convexity preserve uniform domains. Theorem 1: Let \((X_i,d_i)\), \(i= 1, 2\), be proper metric spaces, and let \(\Omega_i\subset X_i\) be open subsets with \(\partial\Omega_1\neq\emptyset\). Let \(h:\Omega_1\to \Omega_2\) be an \(\eta\)-quasi-Möbius homeomorphism. If \(\Omega_1\) is \(c_1\)-uniform and \((X_2,d_2)\) is \(c_2\)-quasiconvex and \(c_2\)-annular convex, then \(\Omega_2\) is \(c\)-uniform with \(c= c(\eta,c_1, c_2)\).