The aggregation, arrangement and bonding together of a set of components to form an extracellular vesicular exosome, a membrane-bounded vesicle that is released into the extracellular region by fusion of the limiting endosomal membrane of a multivesicular body with the plasma membrane. Exosomes are defined by their size, which generally ranges from 30 nm to 100 nm. [ http://www.ncbi.nlm.nih.gov/pubmed/19442504 http://www.ncbi.nlm.nih.gov/pubmed/27462458 ]