An efficient procedure for the fabrication of highly conductive carbon nanotube/graphene hybrid yarns has been developed. To start, arrays of vertically aligned multi-walled carbon nanotubes (MWNT) are converted into indefinitely long MWNT sheets by drawing. Graphene flakes are then deposited onto the MWNT sheets by electrospinning to form a composite structure that is transformed into yarn filaments by twisting. The process is scalable for yarn fabrication on an industrial scale. Prepared materials are characterized by electron microscopy, electrical, mechanical, and electrochemical measurements. It is found that the electrical conductivity of the composite MWNT-graphene yarns is over 900 S/cm. This value is 400% and 1250% higher than electrical conductivity of pristine MWNT yarns or graphene paper, respectively. The increase in conductivity is asssociated with the increase of the density of states near the Fermi level by a factor of 100 and a decrease in the hopping distance by an order of magnitude induced by grapene flakes. It is found also that the MWNT-graphene yarn has a strong electrochemical response with specific capacitance in excess of 111 Fg-1. This value is 425% higher than the capacitance of pristine MWNT yarn. Such substantial improvements of key properties of the hybrid material can be associated with the synergy of MWNT and graphene layers in the yarn structure. Prepared hybrid yarns can benefit such applications as high-performance supercapacitors, batteries, high current capable cables, and artificial muscles.