A fragment-based method for computing protein-ligand binding free energies by systematic sampling has been developed. Systematic sampling of fragment-protein interactions in translations and rotational space is followed by de novo assembly of fragments into molecules and computation of binding free energies for the molecules with statistical mechanics. The rigorous sampling provides independence from the choice of initial binding pose and assembling fragments enables evaluation of binding of a large number of molecule poses with relatively little computation. The method allows a full sampling of possible conformations and avoids the "conformational focusing" problem associated with free energy methods that sample only limited conformational and orientation changes from a starting pose. The direct computation of the entropy loss upon assembling fragments into molecules is an innovation for fragment-based methods. The computed binding free energies are compared to calorimetric data for a series of ligands for the T4 lysozyme L99A mutant and binding constants for a series of p38 MAP kinase ligands. In both cases, the standard error of prediction is close to 1 kcal/mol.