The present invention relates to woven tubular nanotextiles, fabrication thereof using a weaving apparatus, and use thereof in vascular graft applications. The woven nanotextile conduit is 0.1 to 50 mm in diameter and includes a multitude of hierarchically arranged nanofibers. They are made from low strength bundled nanoyarns containing thousands of nanofibers with improved mechanical strength. The weaving apparatus interweaves the warp and weft yarns in longitudinal and transverse directions, resulting in a flexible and strong woven product. The physical and biological properties of the woven nanotextile were significantly enhanced when compared to non-woven nanofibrous form and conventional medical textiles. The nanotextile displayed superhydrophilic behavior in an otherwise hydrophobic material and when implanted as a vascular graft was robust, suturable, kink-proof and non-thrombogenic, with complete endothelialization of the graft luminal area.