We develop the deformation theory of instantons on asymptotically conicalG2-manifolds, where an asymptotic connection at infinity is fixed. A spinorial approach is adopted to relate the space of deformations to the kernel of a twisted Dirac operator on theG2-manifold and to the eigenvalues of a twisted Dirac operator on the nearly Kähler link. This framework is then used to calculate the virtual dimension of the moduli spaces ofG2-instantons on which several known examples live. One such example considered is theG2-instanton of Günaydin-Nicolai, which lives onR7.As an application of the deformation theory, we show how knowledge of the virtual dimension of the moduli space allows us to prove that unobstructed connections in the moduli space areG2-invariant. By classifying such connections we prove a uniqueness result for unobstructedG2-instantons on the principalG2-bundleoverR7.