I'd use one of 2 methods.
1. Gonzo42's advice is good, but I'd use the largest
T-nuts I could, installed from the back side of the backing board. You can attach the mount using short screws to match the T-nuts.
2. Build a cabinet enclosing the entire area of the shelf with one or two cabinet doors. You could put the mount on the single door or on the a vertical stile between the two doors using T-nuts. That would allow you cabinet space for other video accessories and/or DVD's, etc. You could add a hole through the stile or through the single door to allow cables from the TV to connect to the outlets inside the cabinet. One slight drawback would be having to open the cabinet door to adjust the antenna position.