The human gut microbiome is a complex ecosystem that both affects and is affected by its host status. Previous analyses of gut microflora revealed associations between specific microbes and host health and disease status, genotype and diet. Here, we developed a method of predicting biological age of the host based on the microbiological profiles of gut microbiota using a curated dataset of 1,165 healthy individuals (3,663 microbiome samples). Our predictive model, a human microbiome clock, has an architecture of a deep neural network and achieves the accuracy of 3.94 years mean absolute error in cross-validation. The performance of the deep microbiome clock was also evaluated on several additional populations. We further introduce a platform for biological interpretation of individual microbial features used in age models, which relies on permutation feature importance and accumulated local effects. This approach has allowed us to define two lists of 95 intestinal biomarkers of human aging. We further show that this list can be reduced to 39 taxa that convey the most information on their host's aging. Overall, we show that (a) microbiological profiles can be used to predict human age; and (b) microbial features selected by models are age-related.