Here is some professional advice from the ABC Certified Dog Trainer program for preventing your dog from continuing to dig. Note that these tips are based on the dog already having dug holes around the yard.
Without the dog seeing you, fill the already-created holes up with pieces of the dog's stool and lava rocks. Then, cover the poop and rocks with about one inch of dirt. Dogs will often dig in the same general area, so when the dog goes to dig there again, he will find it unpleasant and will either stop immediately or move to a new spot. If he moves to a new spot, just continue to fill the new holes. The dog should stop within a period of no more than two weeks.
Dog training against this behavior involves never letting the dog see you planting or working in the garden. In addition, do not let him see you filling in holes he has already dug. If the dog sees you digging, it is only natural for him to assume it is acceptable behavior and mimic you.
When you see the dog out in the back yard engaging in proper behavior (e.g. chewing on his toys, sunning himself, etc.), praise that behavior. Remember that to effectively train dogs, the more you positively reinforce a behavior, the stronger that behavior is going to be and the greater the likelihood that the dog will engage in it, both when you are there and when you are not. Work on obedience with your dog on a daily basis. The more you master as a team, the better his behavior will be. You are not only his animal trainer, but his best friend, too.