Multigene panel testing allows many cancer-causing genes to be tested efficiently leading to a larger number of mutation carriers being identified. It is crucial to counsel the carriers on their cancer risks. The counseling hinges on estimates of penetrance, i.e., age-specific risk of developing a cancer associated with a specific gene mutation. We propose a meta-analysis approach based on a Bayesian hierarchical random-effects model to obtain penetrance estimates that can integrate studies reporting different types of risk measures (e.g., penetrance, relative risk, odds ratio) while accounting for associated uncertainties. After estimating posterior distributions of parameters via a Markov chain Monte Carlo algorithm, we estimate penetrance and credible intervals. We investigate the proposed method and compare with an existing approach via simulations based on studies reporting risks for two moderate-risk breast cancer genes, ATM and PALB2. Our method performs well in terms of coverage probability of credible intervals and mean square error of estimates. Finally, we apply our method to estimate the penetrance of breast cancer among carriers of pathogenic mutations in the ATM gene.