An insertion tool is used to implant a knotless suture anchor to secure soft tissue to a rigid structure such as bone. The anchor has an inner member that receives suture thread and rotates within an outer tubular member. An inner shaft on the insertion tool engages the inner tubular member and is used to rotate the inner tubular member so that the suture thread is wrapped onto the inner tubular member thereby increasing contact with the outer tubular member of the anchor which applies pressure to the wrapped suture thread to retain it in position on the inner tubular member while simultaneously and adjustably tensioning the suture thread. The insertion tool has an outer shaft that engages the outer tubular member of the anchor and prevents the outer tubular member from rotating as the inner shaft on the insertion tool rotates the inner tubular member on the anchor.