Authors’ abstract: We prove two versions of Bochner’s theorem for locally compact quantum groups. First, every completely positive definite ‘function’ on a locally compact quantum group \(\mathbb G\) arises as a transform of a positive functional on the universal \(C^*\)-algebra \(C^u_0(\hat{\mathbb G})\) of the dual quantum group. Second, when \(\mathbb G\) is coamenable, complete positive definiteness may be replaced with the weaker notion of positive definiteness, which models the classical notion. A counterexample is given to show that the latter result is not true in general. To prove these results, we show two auxiliary results of independent interest: products are linearly dense in \(L^1_\sharp(\mathbb G)\), and when \(\mathbb G\) is coamenable, the Banach \(*\)-algebra \(L^1_\sharp(\mathbb G)\) has a contractive bounded approximate identity.