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 {\em 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 {\em 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 {\em 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 {\em Planck} baseline, which can reasonably be evaded within the context of modified gravity theories.