Abstract: The invention introduces a connection system for connecting a shaft of a wind tower to a support surface, by means of a shaft, a foundation cage and a plurality of pairs of tendons wherein each tendon has a lower anchoring adapted for the placement thereof inside the foundation, an upper anchoring, at least one strand with a first end and a second end, the strand extending from the upper anchoring to the lower anchoring, a pair of sleeves for each strand, a sleeve fixed to the upper anchoring and a sleeve fixed to the lower anchoring, each sleeve housing a segment of the strand. Additionally, the system introduces a method for connecting a shaft of a wind tower to a support surface.