How do I train my Corgi not to run away?

only one way to cure his natural instinct, invisible fence
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If he isn't already neutered, have it done.
You never want your dog off-lead unless he is in an enclosed area and you are supervising him (ie. dogpark). You don't want him to dash into the street infront of a car, or follow his nose somewhere.
Because you cannot trust your dog off-lead, start with recall in the house or in the yard. Make a noise to get his attention, and call him to you. When he comes, praise him and reward him.
Be consistent.
Then you can go out in the field and continue this (when you feel more comfortable), don't take him off-lead yet, get a long lead, like a 20 ft., and continue practicing.
In time this should work, if not invest in some obedience classes.

And if all else fails, always keep him on-lead, but just have a longer lead if you go out in the field.
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Have a fenced yard or keep him on the leash. You cannot trust a dog if there is something that he wants to go see.Most places have a leash law.
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He needs obedience training. And he may need a repeat class if he had basic obedience when he was young. Corgis are smart, but also stubborn. You must be the leader or they will ignore you. I had to take my 5 year old Corgi rescue back for basic obedience just last year after we fostered several unruly Corgis.

He had to learn "come here" and "leave it" and "stay" all over again. We live in a rural area and these commands are crucial.

He had to learn again that other dogs also are expected to mind, not just him, and that some commands are non-negotiable. From my experience, group sessions by a top quality trainer work very well for Corgis and reinforce the lessons better than any other option. You then must continue using the commands and sometimes treating and reinforcing the training forever.

Two good sources for excellent trainers
http://www.apdt.com/
http://www.nadoi.org/index.htm
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Corgi rescue volunteer