I present the cosmological predictions of two non-local modifications of General Relativity recently proposed by our group, the so-called RT and RR models. Both models have the same number of parameters as Lambda-CDM, with a mass parameter m replacing the cosmological constant. In implementing their cosmological background and perturbations equations into the CLASS Boltzmann code, we constrain the non-local models using the Planck 2015, isotropic and anisotropic BAO, JLA supernovae, H_0 measurements and growth rate data.