We study the cosmological predictions of two recently proposed non-local modifications of General Relativity. Both models have the same number of parameters as LCDM, with a mass parameter m replacing the cosmological constant. We implement the cosmological perturbations of the non-local models into a modification of the CLASS Boltzmann code, and we make a full comparison to CMB, BAO and supernova data. We find that the non-local models fit these datasets as well as LCDM. For both non-local models parameter estimation using Planck+JLA+BAO data gives a value of H_0 higher than in LCDM, and in better agreement with the values obtained from local measurements.