A wearable electronic device may be formed from a layer of fabric having opposing first and second ends. The ends may have first and second respective ear openings that receive a user's ears and may have speakers for playing audio. A soft central portion of the fabric between the ends may overlap the user's eyes. The wearable electronic device may have control circuitry that receives power from a power source. Sensors may be used to gather sensor information such as biometric sensor information. The sensors, control circuitry, and power source may be mounted in a stiff edge portion of the fabric. The stiff edge portion of the fabric may have an elongated strip shape and may extend along an upper edge of the central and the electronic device. Stiffener structures sandwiched between inner and outer layers of the fabric may be used to support speakers.