Place Great Northern beans into a large container and cover with several inches of cool water; let stand for 8 hours to overnight. Drain and transfer beans to a large stockpot.

Add ham hocks, 5 cups water, celery, onion, carrot, garlic, thyme, black pepper, and bay leaf to beans in the stockpot; bring to a boil. Reduce heat to medium-low and simmer until ham falls off the bones, about 2 hours.

Remove ham hocks from soup. Cut meat from bones, discarding fat and bones. Return meat to the pot. Continue cooking until beans reach desired softness.