The theoretical framework of cosmology is mainly defined by gravity, of which general relativity is the current model. Recent tests of general relativity within the Lambda Cold Dark Matter (Lambda CDM) model have found a concordance between predictions and the observations of the growth rate and clustering of the cosmic web(1,2). General relativity has not hitherto been tested on cosmological scales independently of the assumptions of the Lambda CDM model. Here we report an observation of the gravitational redshift of light coming from galaxies in clusters at the 99 per cent confidence level, based on archival data(3). Our measurement agrees with the predictions of general relativity and its modification created to explain cosmic acceleration without the need for dark energy (the f(R) theory(4)), but is inconsistent with alternative models designed to avoid the presence of dark matter(5,6).