We present a multi-task learning approach to jointly estimate the means of multiple independent data sets. The proposed multi-task averaging (MTA) algorithm results in a convex combination of the single-task averages. We derive the optimal amount of regularization, and show that it can be effectively estimated. Simulations and real data experiments demonstrate that MTA both maximum likelihood and James-Stein estimators, and that our approach to estimating the amount of regularization rivals cross-validation in performance but is more computationally efficient.