A surface-mounted veneer anchor is disclosed. The anchoring system has a unique combination of a masonry anchor, a box tie member, and a facing anchor is provided. The primary components of the veneer anchor are wire formatives and provide a closed loop, wire-to-wire connections therebetween. In one embodiment, the inner wythe is constructed from a masonry block material, the masonry anchor has a baseplate with a wire formative attached thereto having elongated eye wire extensions. The elongated eye wires extend into the cavity between the wythes. Each pair of eye wires accommodates the threading thereonto of a box tie through the open end of the box tie. The box tie is then positioned so that the open end is utilizable as part of the facing anchor. The baseplate of the masonry anchor is surface-mounted onto the masonry block of the interior wythe. The facing anchor has a straight wire run and mounted along the exterior wythe to receive the open end of wire box tie with each leg thereof being placed adjacent one side of reinforcement wire. The facing anchor is embedded in a bed joint of the exterior wythe. As the elongated eye wires have sealed eyelets or loops and the open ends of the box ties are sealed in the joints of the exterior wythes, a positive, closed-loop interengagement results.