Free energies govern the behavior of soft and liquid matter, and improving their predictions could have a large impact on the development of drugs, electrolytes and homogeneous catalysts. Unfortunately, it is challenging to devise an accurate description of effects governing solvation such as hydrogen-bonding, van der Waals interactions, or entropy and conformational sampling. We present a Free energy Machine Learning (FML) model applicable throughout chemical compound space and based on a representation that employs computationally efficient Boltzmann averages for an approximated sampling of configurational space. Using the FreeSolv database, FML's out-of-sample prediction errors of experimental hydration free energies decay systematically with training set size, and experimental uncertainty (0.6 kcal/mol) is reached after training on 80% (490 molecules).Corresponding FML model errors are on par or better than state-of-the art, physics based, legacy approaches. To generate the input representation for a new query compound, the FML requires approximate and short molecular dynamics runs. We showcase the usefulness of FML through analysis of predicted solvation free energies for 116k organic molecules (all force-field compatible molecules in QM9 database) identifying the most and least solvated systems, and rediscovering quasi-linear structure property relationships in terms of hydrogen-bond donors, number of NH or OH groups, number of oxygen atoms in hydrocarbons, and number of heavy atoms.FML's accuracy is maximal when the temperature used for the molecular dynamics simulation to generate averaged input representation samples in training is the same as for the query compounds. The sampling time for the representation converges with respect to the model's prediction error for both, training and testing.