The process in which autophagosomes, double-membraned vesicles containing cytoplasmic material, fuse with a vacuole (yeast) or lysosome (e.g. mammals and insects). In the case of yeast, inner membrane-bounded structures (autophagic bodies) appear in the vacuole. Fusion provides an acidic environment and digestive function to the interior of the autophagosome. [ http://www.ncbi.nlm.nih.gov/pubmed/28077293 ]