The growing demand for wearable electronics requires flexible and stretchable conductive materials. Among them, carbon nanotubes are recognized for their outstanding mechanical, electrical, optical properties and chemical stability. In this paper, we introduce a novel technique of carbon nanotube fiber fabrication, which we named Wet Pulling. The method allows straightforward fiber production out of carbon nanotube thin films, collected on a filter after the synthesis or deposited onto any substrate. It relies on a combination of film and solvent properties. The wet pulling technique has prominent advantages that make it a promising candidate for both small and large-scale production of CNT fibers with desired properties. The method is also easily adaptive to different kinds of carbon nanotubes and allows rapid fabrication of both active and passive flexible electronic components. A tactile sensor, a pulsometer and an electrical circuit are fabricated for the demonstration of their applicability. We expect this new approach to simplify the production of functional carbon nanotube fibers and to enlarge their usage in diverse applications.