Using a masonry bit, drill pilot holes at the location for screw-fasteners. Then insert masonry anchors into those hole and screw the screws down throught he threshold. The pressure created from screwing the screw into the anchor grips the sides of the pilot hole so as to hold the anchor in place.
PL Premium polyurethyne construction adhesive is the best glue on the face of the earth, IMO and will practically weld your wood threshold to the concrete. Squeeze a bead or three under where the thresh will go and smack it down into the glue. Weight it in place overnite and you be fine.