Diblock copolymers are known to spontaneously organize into polymer vesicles. Typically, this is achieved through the techniques of film rehydration or electroformation. We present a new method for generating polymer vesicles from double emulsions. We generate precision water-in-oil-in-water double emulsions from the breakup of concentric fluid streams; the hydrophobic fluid is a volatile mixture of organic solvent that contains dissolved diblock copolymers. We collect the double emulsions and slowly evaporate the organic solvent, which ultimately directs the self-assembly of the dissolved diblock copolymers into vesicular structures. Independent control over all three fluid streams enables precision assembly of polymer vesicles and provides for highly efficient encapsulation of active ingredients within the polymerosomes. We also use double emulsions with several internal drops to form new polymerosome structures.