Coat slow-cooker bowl with nonstick cooking spray.
Drain beans and add to slow cooker bowl. Stir in 6 cups water, ham, onion, celery, carrots, tomatoes and thyme. Cover and cook on LOW for 10 hours.
Remove 2 cups of the soup, puree and return to slow cooker. Add salt and pepper; gradually add spinach and stir until wilted.