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. For both non-local models, Bayesian parameter estimations that include Planck data generically give a value of H_0 higher than in Lambda-CDM, and in better agreement with the values obtained from local measurements. We also perform a Bayesian model comparison between the RT, RR and Lambda-CDM models, using the Savage-Dickey density ratio method. We find that, in the framework of the so-called Planck baseline, the RT model performs as well as Lambda-CDM whereas the RR model is disfavored. We finally show that the latter conclusion significantly depends on the prior choice which is assumed by the Planck baseline, which can however reasonably be evaded within the context of modified gravity theories.