Bayesian estimation of divergence times from molecular sequences relies on sophisticated Markov chain Monte Carlo techniques, and Metropolis-Hastings (MH) samplers have been successfully used in that context. This approach involves heavy computational burdens that can hinder the analysis of large phylogenomic data sets. Reliable estimation of divergence times can also be extremely time consuming, if not impossible, for sequence alignments that convey weak or conflicting phylogenetic signals, emphasizing the need for more efficient sampling methods. This article describes a new approach that estimates the posterior density of substitution rates and node times. The prior distribution of rates accounts for their potential autocorrelation along lineages, whereas priors on node ages are modeled with uniform densities. Also, the likelihood function is approximated by a multivariate normal density. The combination of these components leads to convenient mathematical simplifications, allowing the posterior distribution of rates and times to be estimated using a Gibbs sampling algorithm. The analysis of four real-world data sets shows that this sampler outperforms the standard MH approach and demonstrates the suitability of this new method for analyzing large and/or difficult data sets.