Place Great Northern beans into a large container and cover with several inches of cool water; let stand 8 hours to overnight. Drain water and transfer beans to a large stockpot.
Mix ham hocks, water, celery, onion, carrot, garlic, thyme, black pepper, and bay leaf with beans in the stockpot; bring to a boil. Reduce heat to medium low and simmer until ham is coming 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.