Heat olive oil in a large pot over medium-high heat. Add hot sausage, mild sausage, salt, and pepper; cook, breaking up sausage with the back of a wooden spoon, until no longer pink, about 5 minutes.
Stir onion and celery into the pot; cook and stir until onion is soft and translucent, about 5 minutes. Stir in garlic until fragrant, about 30 seconds. Add chicken broth, sweet potato, and bay leaf. Bring to a boil; cook over medium-high heat for 10 minutes.
Stir great northern beans and diced tomatoes into the pot. Cook until beans are heated through and sweet potato is soft, about 10 minutes. Add kale; simmer until wilted, about 5 minutes.